Question

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?

Answer 1

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.