Question

Find the new coordinates of a point P (3, 2) if it is rotated 90 degrees in counterclockwise direction with respect to the origin
A. (-2,3)
B. (-2,-3)
C. (-3,3)
D. (-3,2)
E. (-3,-2)

Answer 1

Hint:When a point is rotated through \[{90^ \circ }\] about the origin in the clockwise direction then the point \[M(h,k)\] takes the image \[M'(k, - h)\] and when the point is rotated through \[{90^\circ }\] about the origin in the counterclockwise direction then the point \[M(h,k)\] takes the image \[M'( - k,h)\] . In this question we are given a point which is rotated by \[{90^ \circ }\] in counterclockwise direction so we will find the new coordinate after rotation about the origin.

Complete step by step solution:
Given the point whose new coordinate is to be found is \[P\left( {3,2} \right)\]
Let the new coordinate of point after the rotation be \[P'\]
Now we know when the point is rotated through \[{90^ \circ }\] about the origin in the counterclockwise direction then the point \[M(h,k)\] takes the image \[M'( - k,h)\] .
Now since after rotations of the point \[M(h,k)\] takes the image \[M'( - k,h)\] , hence we can write the new coordinate of the point \[P\] will be
 \[
\because M(h,k) \to M'( - k,h) \\
\therefore P\left( {3,2} \right) \to P'\left( { - 2,3} \right) \\
\]
Therefore the new coordinates of a point P (3, 2) if it is rotated 90 degrees in counterclockwise direction with respect to the origin will be \[P'\left( { - 2,3} \right)\]

Option A is correct.

Note: In the coordinate of a point \[A(h,k)\] , \[h\] means a point on the x-axis of a two dimensional graph and \[k\] is a point on the y-axis of a two dimensional graph.
We can also solve this problem by plotting the point \[P\left( {3,2} \right)\] on a two dimensional graph and then rotating that point by \[{90^ \circ }\] about the origin in the counterclockwise direction.