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.

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