Question

Triangle ABC has the coordinates A(8,4) B(12,4) C(16,12). If the triangle is dilated with a scale factor of 4, what are the new coordinates?

A. A’(32,16) B’(48,16) C’(64,48)

B. A’(4,0) B’(8,0) C’(12,8)

C. A’(12,8) B’(16,8) C’(20,16)


D. A’(2,1) B’(2,1) C’(4,3)

Answer 1

A. A'(32, 16) B'(48, 16) C'(64, 48)

Explanation:

Dilation is a transformation in geometry that changes the size of a figure while preserving its shape. It involves multiplying the coordinates of each point by a scale factor relative to a fixed center of dilation to create a new figure that is either larger or smaller than the original. The center of dilation serves as the fixed point around which the figure is expanded or contracted.

To dilate a figure where the center of dilation is the origin (0, 0), simply multiply each coordinate point by the scale factor.

In this case, as we have not been given a center of dilation, so we can assume it is the origin. The given scale factor is 4.

Given coordinates of the vertices of triangle ABC:

• A (8, 4)
• B (12, 4)
• C (16, 12)

To find the new coordinates after dilation with the origin as the center of dilation, multiply each coordinate point by the scale factor of 4.

A' = (8 · 4, 4 · 4) = (32, 16)

B' = (12 · 4, 4 · 4) = (48, 16)

C' = (16 · 4, 12 · 4) = (64, 48)

Therefore, the new coordinates of the dilated triangle are:

• A' (32, 16)
• B' (48, 16)
• C' (64, 48)