Question

PQ

¯¯¯¯¯¯¯¯ PQ ¯  has endpoints at P (-2,3) and Q (4,1). The center of dilation is (-1,4) and the scale factor is 2. What are the coordinates of the endpoints of P'Q'?

Answer 1

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).