Join two points P(2,2) and Q(4,2) in a plane. Fixed the point P and rotate the line PQ in anti-Clockwise direction at an angle of 270 degree. Find the new coordinates of point Q. Also, Find the area formed by this figure. 

Asked by venkat34 | 6th Jan, 2016, 11:27: PM

Expert Answer:

Let the new coordinates of Point Q be Q'
Q' = (2,0).
We need to find the area formed by the points P, Q and Q', i.e, area of triangle PQQ'.
begin mathsize 16px style angle QPQ apostrophe equals space 90 degree end style
Hence, triangle PQQ' is a right angled triangle.
Also, we know that PQ = PQ' = 2 units
begin mathsize 16px style Area space of space increment PQQ apostrophe space equals space 1 half cross times PQ cross times PQ apostrophe space equals space 1 half cross times 2 cross times 2 space equals space 2 space sq. space units end style

Answered by Kajal Gupta | 7th Jan, 2016, 12:27: PM