Points A and B are at (3 ,8 ) and (7 ,3 ), respectively. Point A is rotated counterclockwise about the origin by pi and dilated about point C by a factor of 5 . If point A is now at point B, what are the coordinates of point C?

1 Answer
Apr 18, 2018

C=(-11/2,43/(-4))

Explanation:

Here Point A=(3,8).
Rotating 'bout the origin by pi gives A'(-3,-8)

Again if the point A' is dilated through the center C with scale factor 5 yield it's next point a point B (7,3).

We know dilation of the coordinates are,Let k be the scale factor and (a,b) be the point C.
x'=k (x-a)+a
y'=k (y-b)+b

For a,
x'=k (x-a)+a
or, 7=5 (-3-a)+a
:.a=-11/2

For b,
y'=k (y-b)+b
3=5 (-8-b)+b
:.b=-43/4

Hence C (-11/2,-43/4) is the required point of dilation.