To determine the type of triangle formed by the points (-4, 0), (4, 0), and (0, 3), we will calculate the lengths of the sides using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²) Let the points be A(-4, 0), B(4, 0), anRead more
To determine the type of triangle formed by the points (-4, 0), (4, 0), and (0, 3), we will calculate the lengths of the sides using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
Let the points be A(-4, 0), B(4, 0), and C(0, 3).
1. Calculate the length of side AB:
AB = √((4 – (-4))² + (0 – 0)²)
= √((4 + 4)² + 0²)
= √(8²)
= √64
= 8
2. Calculate the length of side BC:
BC = √((0 – 4)² + (3 – 0)²)
= √((-4)² + 3²)
= √(16 + 9)
= √25
= 5
3. Calculate the length of side AC:
AC = √((0 – (-4))² + (3 – 0)²)
= √((0 + 4)² + 3²)
= √(4² + 3²)
= √(16 + 9)
= √25
= 5
Now that we have the side lengths:
AB = 8, BC = 5, AC = 5.
Since two sides (BC and AC) are equal, the triangle is **isosceles**. Additionally, we can check if it forms a right triangle using the Pythagorean theorem:
For a right triangle, the square of the longest side (hypotenuse) should equal the sum of the squares of the other two sides. Here, AB is the longest side.
Since the Pythagorean theorem does not hold, the triangle is not a right triangle. It is also not equilateral because all sides are not equal. Therefore, the correct answer is:
b) isosceles triangle
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
To solve for the value of p, we use the distance formula between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²) Here, the points are (4, p) and (1, 0), and the distance is given as 5. Substituting into the formula: 5 = √((1 - 4)² + (0 - p)²) Simplify the terms inside the square rooRead more
To solve for the value of p, we use the distance formula between two points (x₁, y₁) and (x₂, y₂):
d = √((x₂ – x₁)² + (y₂ – y₁)²)
Here, the points are (4, p) and (1, 0), and the distance is given as 5. Substituting into the formula:
5 = √((1 – 4)² + (0 – p)²)
Simplify the terms inside the square root:
5 = √((-3)² + (-p)²)
5 = √(9 + p²)
Square both sides to eliminate the square root:
5² = 9 + p²
25 = 9 + p²
Rearrange the equation to isolate p²:
p² = 25 – 9
p² = 16
Take the square root of both sides:
p = ±√16
p = ±4
Thus, the value of p can be either +4 or -4.
The correct answer is:
b) ±4
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²) ### StepRead more
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
### Step 1: Calculate the lengths of all sides
1. Length of AB:
AB = √((9 – 9)² + (6 – 0)²)
= √(0² + 6²)
= √36
= 6
4. Length of DA:
DA = √((9 – (-9))² + (0 – 0)²)
= √((9 + 9)² + 0²)
= √324
= 18
Step 2: Analyze the side lengths
From the calculations:
– AB = CD = 6 (opposite sides are equal)
– BC = DA = 18 (opposite sides are equal)
Thus, the quadrilateral has opposite sides that are equal in length.
Step 3: Check if the angles are right angles
To confirm whether the angles are right angles, we calculate the slopes of adjacent sides and check if their product is -1 (indicating perpendicularity).
1. Slope of AB:
Slope of AB = (6 – 0) / (9 – 9) = undefined (vertical line)
2. Slope of BC:
Slope of BC = (6 – 6) / (-9 – 9) = 0 (horizontal line)
3. Slope of CD:
Slope of CD = (0 – 6) / (-9 – (-9)) = undefined (vertical line)
4. Slope of DA:
Slope of DA = (0 – 0) / (9 – (-9)) = 0 (horizontal line)
Since the slopes of adjacent sides (e.g., AB and BC, or BC and CD) indicate perpendicularity (one is vertical and the other is horizontal), all angles are right angles.
Step 4: Conclusion
The quadrilateral has opposite sides equal and all angles are right angles. Therefore, it is a **rectangle**.
The correct answer is:
b) rectangle
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate. Given the point (-6, 8), the y-coordinate isRead more
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate.
Given the point (-6, 8), the y-coordinate is 8. The distance from the x-axis is:
Distance = |y| = |8| = 8 units
Thus, the distance of the point (-6, 8) from the x-axis is 8 units.
The correct answer is:
c) 8 units
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
To find the point on the x-axis that is equidistant from the points (-1, 0) and (5, 0), let the required point be (x, 0), since it lies on the x-axis (its y-coordinate is 0). Step 1: Use the distance formula The distance between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ -Read more
To find the point on the x-axis that is equidistant from the points (-1, 0) and (5, 0), let the required point be (x, 0), since it lies on the x-axis (its y-coordinate is 0).
Step 1: Use the distance formula
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
The distances from (x, 0) to (-1, 0) and (5, 0) must be equal. Therefore:
Since both distances are equal, the point (2, 0) is indeed equidistant from (-1, 0) and (5, 0).
The correct answer is:
b) (2, 0)
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
The points (-4, 0), (4, 0) and (0, 3) are the vertices of a
To determine the type of triangle formed by the points (-4, 0), (4, 0), and (0, 3), we will calculate the lengths of the sides using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²) Let the points be A(-4, 0), B(4, 0), anRead more
To determine the type of triangle formed by the points (-4, 0), (4, 0), and (0, 3), we will calculate the lengths of the sides using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
Let the points be A(-4, 0), B(4, 0), and C(0, 3).
1. Calculate the length of side AB:
AB = √((4 – (-4))² + (0 – 0)²)
= √((4 + 4)² + 0²)
= √(8²)
= √64
= 8
2. Calculate the length of side BC:
BC = √((0 – 4)² + (3 – 0)²)
= √((-4)² + 3²)
= √(16 + 9)
= √25
= 5
3. Calculate the length of side AC:
AC = √((0 – (-4))² + (3 – 0)²)
= √((0 + 4)² + 3²)
= √(4² + 3²)
= √(16 + 9)
= √25
= 5
Now that we have the side lengths:
AB = 8, BC = 5, AC = 5.
Since two sides (BC and AC) are equal, the triangle is **isosceles**. Additionally, we can check if it forms a right triangle using the Pythagorean theorem:
For a right triangle, the square of the longest side (hypotenuse) should equal the sum of the squares of the other two sides. Here, AB is the longest side.
Check: AB² = BC² + AC²
8² = 5² + 5²
64 = 25 + 25
64 ≠ 50
Since the Pythagorean theorem does not hold, the triangle is not a right triangle. It is also not equilateral because all sides are not equal. Therefore, the correct answer is:
b) isosceles triangle
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/
If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
To solve for the value of p, we use the distance formula between two points (x₁, y₁) and (x₂, y₂): d = √((x₂ - x₁)² + (y₂ - y₁)²) Here, the points are (4, p) and (1, 0), and the distance is given as 5. Substituting into the formula: 5 = √((1 - 4)² + (0 - p)²) Simplify the terms inside the square rooRead more
To solve for the value of p, we use the distance formula between two points (x₁, y₁) and (x₂, y₂):
d = √((x₂ – x₁)² + (y₂ – y₁)²)
Here, the points are (4, p) and (1, 0), and the distance is given as 5. Substituting into the formula:
5 = √((1 – 4)² + (0 – p)²)
Simplify the terms inside the square root:
5 = √((-3)² + (-p)²)
5 = √(9 + p²)
Square both sides to eliminate the square root:
5² = 9 + p²
25 = 9 + p²
Rearrange the equation to isolate p²:
p² = 25 – 9
p² = 16
Take the square root of both sides:
p = ±√16
p = ±4
Thus, the value of p can be either +4 or -4.
The correct answer is:
b) ±4
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/
The points A (9, 0), B (9, 6), C(-9, 6) and D(-9, 0) are the vertices of a
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ - y₁)²) ### StepRead more
To determine the type of quadrilateral formed by the points A(9, 0), B(9, 6), C(-9, 6), and D(-9, 0), we will analyze the properties of the sides and angles using the distance formula. The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
### Step 1: Calculate the lengths of all sides
1. Length of AB:
AB = √((9 – 9)² + (6 – 0)²)
= √(0² + 6²)
= √36
= 6
2. Length of BC:
BC = √((-9 – 9)² + (6 – 6)²)
= √((-18)² + 0²)
= √324
= 18
3. Length of CD:
CD = √((-9 – (-9))² + (0 – 6)²)
= √(0² + (-6)²)
= √36
= 6
4. Length of DA:
DA = √((9 – (-9))² + (0 – 0)²)
= √((9 + 9)² + 0²)
= √324
= 18
Step 2: Analyze the side lengths
From the calculations:
– AB = CD = 6 (opposite sides are equal)
– BC = DA = 18 (opposite sides are equal)
Thus, the quadrilateral has opposite sides that are equal in length.
Step 3: Check if the angles are right angles
To confirm whether the angles are right angles, we calculate the slopes of adjacent sides and check if their product is -1 (indicating perpendicularity).
1. Slope of AB:
Slope of AB = (6 – 0) / (9 – 9) = undefined (vertical line)
2. Slope of BC:
Slope of BC = (6 – 6) / (-9 – 9) = 0 (horizontal line)
3. Slope of CD:
Slope of CD = (0 – 6) / (-9 – (-9)) = undefined (vertical line)
4. Slope of DA:
Slope of DA = (0 – 0) / (9 – (-9)) = 0 (horizontal line)
Since the slopes of adjacent sides (e.g., AB and BC, or BC and CD) indicate perpendicularity (one is vertical and the other is horizontal), all angles are right angles.
Step 4: Conclusion
The quadrilateral has opposite sides equal and all angles are right angles. Therefore, it is a **rectangle**.
The correct answer is:
b) rectangle
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/
The distance of the point (-6, 8) from the x-axis is
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate. Given the point (-6, 8), the y-coordinate isRead more
The distance of a point (x, y) from the x-axis is given by the absolute value of its y-coordinate. This is because the x-axis is the horizontal line where y = 0, and the vertical distance between the point and the x-axis depends only on the y-coordinate.
Given the point (-6, 8), the y-coordinate is 8. The distance from the x-axis is:
Distance = |y| = |8| = 8 units
Thus, the distance of the point (-6, 8) from the x-axis is 8 units.
The correct answer is:
c) 8 units
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/
The point on the x-axis which is equidistant from points (-1, 0) and (5, 0) is
To find the point on the x-axis that is equidistant from the points (-1, 0) and (5, 0), let the required point be (x, 0), since it lies on the x-axis (its y-coordinate is 0). Step 1: Use the distance formula The distance between two points (x₁, y₁) and (x₂, y₂) is given by: d = √((x₂ - x₁)² + (y₂ -Read more
To find the point on the x-axis that is equidistant from the points (-1, 0) and (5, 0), let the required point be (x, 0), since it lies on the x-axis (its y-coordinate is 0).
Step 1: Use the distance formula
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
The distances from (x, 0) to (-1, 0) and (5, 0) must be equal. Therefore:
Distance to (-1, 0) = Distance to (5, 0)
√((x – (-1))² + (0 – 0)²) = √((x – 5)² + (0 – 0)²)
Simplify both sides:
√((x + 1)²) = √((x – 5)²)
Step 2: Eliminate the square roots
Square both sides to remove the square roots:
(x + 1)² = (x – 5)²
Expand both sides:
x² + 2x + 1 = x² – 10x + 25
Step 3: Simplify the equation
Cancel out x² from both sides:
2x + 1 = -10x + 25
Combine like terms:
2x + 10x = 25 – 1
12x = 24
Solve for x:
x = 24 / 12
x = 2
Step 4: Verify the solution
The point on the x-axis is (2, 0). To verify, calculate the distances from (2, 0) to (-1, 0) and (5, 0):
1. Distance to (-1, 0):
√((2 – (-1))² + (0 – 0)²) = √((2 + 1)²) = √(3²) = 3
2. Distance to (5, 0):
√((2 – 5)² + (0 – 0)²) = √((-3)²) = √(3²) = 3
Since both distances are equal, the point (2, 0) is indeed equidistant from (-1, 0) and (5, 0).
The correct answer is:
b) (2, 0)
This question related to Chapter 7 Mathematics Class 10th NCERT. From the Chapter 7 Coordinate Geometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-7/