Say we are give a point (x, y) , then the general relationship for all dilation centered at (a, b) with a scale factor of k is given by (a + k(x-a), b+k(y-b)).
In our case a = -1, b = 4, k = 2
For point P(-2, 3) with center of dilation (-1, 4) and scale factor of 2, the point after dilation P' is given by (-1+2(-2-(-1)), 4+2(3-4)).
Simplifying it P' further we get ⇒(-1+2(-2+1), 4+2(-1))
⇒(-1+2(-1), 4-2)
⇒(-1-2, 2)
⇒P' = (-3, 2)
In the same way, For point Q(4, 1) with center of dilation (-1, 4) and scale factor of 2, the point after dilation Q' is given by (-1+2(4-(-1)), 4+2(1-4)).
Simplifying it Q' further we get ⇒(-1+2(4+1), 4+2(-3))
⇒(-1+2(5), 4-6)
⇒(-1+10, -2)
⇒Q' = (9, -2)
So we can conclude coordinates of P' as (-3, 2) and Q' as (9, -2).
