The core principles of reflection remain consistent, but the results would be mirrored vertically. If reflected across the x-axis, all x-coordinates of the triangle's vertices would remain unchanged, while all y-coordinates would switch to their opposites (positive to negative). The size and shape wRead more
The core principles of reflection remain consistent, but the results would be mirrored vertically. If reflected across the x-axis, all x-coordinates of the triangle’s vertices would remain unchanged, while all y-coordinates would switch to their opposites (positive to negative). The size and shape would still be preserved, but the triangle would appear upside down compared to its original position, rather than flipped left-to-right as it was in the y-axis reflection.
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Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
After plotting Z (5, –6) in the fourth quadrant, we construct a right-angled triangle using points I (5, 0) on the x-axis and N (0, 0) at the origin. The vertical side IZ has a length of 6 units, and the horizontal side IN is 5 units. Using the Baudhāyana-Pythagoras Theorem, the hypotenuse ZN lengthRead more
After plotting Z (5, –6) in the fourth quadrant, we construct a right-angled triangle using points I (5, 0) on the x-axis and N (0, 0) at the origin. The vertical side IZ has a length of 6 units, and the horizontal side IN is 5 units. Using the Baudhāyana-Pythagoras Theorem, the hypotenuse ZN length is calculated as the square root of (5 squared plus –6 squared), which equals the square root of 61 units.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
By analyzing the coordinates, we can predict that: (i) AM is horizontal (y = –2) and MP is vertical (x = –5), making them perpendicular. (ii) Side AM is parallel to the x-axis because its y-coordinates are constant. (iii) Points M(–5, –2) and P(–5, 2) have the same x-value but opposite y-values, makRead more
By analyzing the coordinates, we can predict that: (i) AM is horizontal (y = –2) and MP is vertical (x = –5), making them perpendicular. (ii) Side AM is parallel to the x-axis because its y-coordinates are constant. (iii) Points M(–5, –2) and P(–5, 2) have the same x-value but opposite y-values, making them mirror images across the x-axis. Plotting these points on a Cartesian plane confirms that RAMP forms a quadrilateral with these properties.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
A coordinate system without negative numbers would be limited to the "positive" directions (right and up) from the origin. Historically, the formalization of zero and negative numbers by Indian mathematicians like Brahmagupta was essential for creating the modern four-quadrant Cartesian plane. WithoRead more
A coordinate system without negative numbers would be limited to the “positive” directions (right and up) from the origin. Historically, the formalization of zero and negative numbers by Indian mathematicians like Brahmagupta was essential for creating the modern four-quadrant Cartesian plane. Without these negative values, we could only describe points in Quadrant I, meaning most of the infinite 2-D plane would remain unreachable and unlocatable.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
To check if points are collinear without plotting, you can use the ratio method. For points passing through the origin A (0, 0), if the ratio of the y-coordinate to the x-coordinate for all other points is equal, they lie on the same straight line. For the point M (–3, –4), the ratio is 4/3 and forRead more
To check if points are collinear without plotting, you can use the ratio method. For points passing through the origin A (0, 0), if the ratio of the y-coordinate to the x-coordinate for all other points is equal, they lie on the same straight line. For the point M (–3, –4), the ratio is 4/3 and for the point G (6, 8), the ratio is also 4/3. Thus, M, A and G are collinear.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
Would these observations be the same if ΔADM is reflected in the x-axis (instead of the y-axis)?
The core principles of reflection remain consistent, but the results would be mirrored vertically. If reflected across the x-axis, all x-coordinates of the triangle's vertices would remain unchanged, while all y-coordinates would switch to their opposites (positive to negative). The size and shape wRead more
The core principles of reflection remain consistent, but the results would be mirrored vertically. If reflected across the x-axis, all x-coordinates of the triangle’s vertices would remain unchanged, while all y-coordinates would switch to their opposites (positive to negative). The size and shape would still be preserved, but the triangle would appear upside down compared to its original position, rather than flipped left-to-right as it was in the y-axis reflection.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessPlot point Z (5, – 6) on the Cartesian plane. Construct a right-angled triangle IZN and find the lengths of the three sides. (Comment: Answers may differ from person to person.)
After plotting Z (5, –6) in the fourth quadrant, we construct a right-angled triangle using points I (5, 0) on the x-axis and N (0, 0) at the origin. The vertical side IZ has a length of 6 units, and the horizontal side IN is 5 units. Using the Baudhāyana-Pythagoras Theorem, the hypotenuse ZN lengthRead more
After plotting Z (5, –6) in the fourth quadrant, we construct a right-angled triangle using points I (5, 0) on the x-axis and N (0, 0) at the origin. The vertical side IZ has a length of 6 units, and the horizontal side IN is 5 units. Using the Baudhāyana-Pythagoras Theorem, the hypotenuse ZN length is calculated as the square root of (5 squared plus –6 squared), which equals the square root of 61 units.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessConsider the points R (3, 0), A (0, – 2), M (– 5, – 2) and P (– 5, 2). If they are joined in the same order, predict: (i) Two sides of RAMP that are perpendicular to each other. (ii) One side of RAMP that is parallel to one of the axes. (iii) Two points that are mirror images of each other in one axis. Which axis will this be? Now plot the points and verify your predictions.
By analyzing the coordinates, we can predict that: (i) AM is horizontal (y = –2) and MP is vertical (x = –5), making them perpendicular. (ii) Side AM is parallel to the x-axis because its y-coordinates are constant. (iii) Points M(–5, –2) and P(–5, 2) have the same x-value but opposite y-values, makRead more
By analyzing the coordinates, we can predict that: (i) AM is horizontal (y = –2) and MP is vertical (x = –5), making them perpendicular. (ii) Side AM is parallel to the x-axis because its y-coordinates are constant. (iii) Points M(–5, –2) and P(–5, 2) have the same x-value but opposite y-values, making them mirror images across the x-axis. Plotting these points on a Cartesian plane confirms that RAMP forms a quadrilateral with these properties.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessWhat would a system of coordinates be like if we did not have negative numbers? Would this system allow us to locate all the points on a 2-D plane?
A coordinate system without negative numbers would be limited to the "positive" directions (right and up) from the origin. Historically, the formalization of zero and negative numbers by Indian mathematicians like Brahmagupta was essential for creating the modern four-quadrant Cartesian plane. WithoRead more
A coordinate system without negative numbers would be limited to the “positive” directions (right and up) from the origin. Historically, the formalization of zero and negative numbers by Indian mathematicians like Brahmagupta was essential for creating the modern four-quadrant Cartesian plane. Without these negative values, we could only describe points in Quadrant I, meaning most of the infinite 2-D plane would remain unreachable and unlocatable.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See lessAre the points M (– 3, – 4), A (0, 0) and G (6, 8) on the same straight line? Suggest a method to check this without plotting and joining the points.
To check if points are collinear without plotting, you can use the ratio method. For points passing through the origin A (0, 0), if the ratio of the y-coordinate to the x-coordinate for all other points is equal, they lie on the same straight line. For the point M (–3, –4), the ratio is 4/3 and forRead more
To check if points are collinear without plotting, you can use the ratio method. For points passing through the origin A (0, 0), if the ratio of the y-coordinate to the x-coordinate for all other points is equal, they lie on the same straight line. For the point M (–3, –4), the ratio is 4/3 and for the point G (6, 8), the ratio is also 4/3. Thus, M, A and G are collinear.
For Detailed Solutions:
Visit NCERT Solutions for Class 9 Ganita Manjari Chapter 1 Orienting Yourself: The Use of Coordinates Question Answer:
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-1/
See less