Accurate and updated NCERT Class 9 Advanced Maths Solutions Chapter 4 Coordinate Geometry Ex 4.1 help students build a strong mathematical foundation.
Ex 4.1 Class 9 Advanced Maths Solutions
Advanced Maths Class 9 Exercise 4.1 Solutions
Exercise 4.1 Class 9 Advanced Maths Solutions
Question 1.
A point P lies in the III quadrant. It is reflected across the 7-axis to create P’ and then P’ is reflected across the X-axis to create P” . In which quadrants does P’ and P” lies?
Solution:
Given, point P lies in the III quadrant.
We know that in the III quadrant, both x and y-coordinates are negative.
Let the coordinates of point P be (-x, -y), where x, y > 0.
Now, P’ is the reflection of P(-x, -y) across the Y-axis.
∴ The coordinates of P’ are (x, -y).
Since, the x-coordinate is positive and the y-coordinate is negative, P’ lies in the IV quadrant.
Further, P” is the reflection of P'(x, -y) across the X-axis.
The coordinates of P’ are (x, y).
Since, both coordinates are positive, P’ lies in the I quadrant.
Hence, P’ lies in the IV quadrant and P’ lies in the I quadrant.
The following figure illustrates the movement of the point across the cartesian plane.
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:
Given, point A has coordinates (a, b).
We know that when a point (x, y) is reflected across the X-axis, its coordinates become (x, -y).
∴ The coordinates of point B are (a, -b).
Given, point Bis exactly 8 units below point A.
So, the difference between the y-coordinate of A and the y-coordinate of B is 8.
∴ b – (-b) = 8
⇒ 2b = 8
⇒ b = 4
Hence, the y-coordinate of point A was 4.
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