Students often refer to NCERT Class 9 Advanced Maths Solutions Chapter 4 Coordinate Geometry Ex 4.1 to verify their answers.
Advanced Maths Class 9 Exercise 4.1 Solutions
Class 9 Advanced Maths Ex 4.1 Solutions
Question 1.
A point P lies in the III quadrant. It is reflected across the y-axis to create P’ and then P’ is reflected across the x-axis to create P”. In which quadrants do P’ and P” lie?
Solution:
A point P in the III quadrant (where x < 0, y < 0) is reflected across the y-axis to create P’, placing it in the IV quadrant (negative x, positive y). Reflecting F across the x-axis creates P”, which moves to the I quadrant (positive x, positive y).
P’ (after reflection in the y-axis): IV Quadrant
P” (after reflection in the x-axis of P’): I Quadrant
Question 2.
A point A(a, b) is reflected across the x-axis to become point B. Point B is exactly 8 units below point A. What was the y-coordinate of point A?
Solution:
When a point is reflected across the x-axis, only the sign of the y-coordinate changes.
So, if A = (a, b), then its reflection is B = (a, -b).
The vertical distance between A and B is:
|b – (-b)| = |2b |
Given that B is exactly 8 units below A, 2b = 8.
Therefore, b = 4.
So, the y-coordinate of point A is 4.