Question

Port A: Under a dilation of scale factor centered at (7.5). SM becomes HG. Determine the coordinates of HG and sketch HG on the graph. The coordinates for HG (2.5,-1.5),(1.5,-1.5) Port B: Under a dilation of scale factor 2 centered at the origin, SM becomes TP. Determine the coordinates of TP and sketch TP on the graph, Part C: Under a dilation of scale factor-centered at (-4,-6). SM becomes CB. Determine the coordinates of CB and sketch CB on the graph.

Answer 1

Part B)

S is located at (-8, -2)

M is located at (-4, -6)

After the dilation is applied centered at (0,0) by a scale factor of 2, we get:

S(-8, -2) -> (-8*2, -2*2) -> T(-16, -4)

M(-4, -6) -> (-4*2, -6*2) -> P(-8, -12)

Part C)

If point A(a,b) is dilated centered at (x,y) with scale factor k:

A' = [k(a - x) + x, k(b - y) + y]

Replacing with points S and M, center of dilation (-4, -6), and k = 1/2, we get:

S(-8, -2) -> 1/2[-8 - (-4)] + (-4), 1/2[-2 - (-6)] + (-6) -> C(-6, -4)

M(-4, -6) -> 1/2[-4 - (-4)] + (-4), 1/2[-6 - (-6)] + (-6) -> B(-4, -6)