Triangle ABC was dilated and translated to form similar triangle A’B’C’.

What is the scale factor of the dilation?

A. 1/5
B. 2/5
C. 5/2
D. 5/1

The scale factor of dilation from ABC to A’B’C’ is 2.5.

Step-by-step explanation:

Step 1:

First, we plot the coordinates of both triangles.

The coordinates of triangle ABC are as follows;

A = (0, 2), B = (2, 2), and C = (2,0).

The coordinates of triangle A’B’C’ are;

A’= (-4, -1), B’= (1, -1), and C’ = (1, -6).

Step 2:

Next, we need to find the distances between at least to coordinates for both triangles.

The distances between vertical lines are found by calculating the difference in y values while for horizontal lines, the distances are found by calculating the difference between the x values.

The distance of AB = 2 - 0 = 2 units, the distance of BC = 2 - 0 = 2 units.

The distance of A’B’ = 1 - (-4) = 5 units, the distance of B’C’ = 6 - 1 = 5 units (both points are negative y)

Step 3:

To calculate the scale factor, we divide the measurement after scaling by the same measurement before scaling.

In this case, it is the length of the AB. So the scale factor = = 2.5.

The scale factor for line BC = = 2.5.

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step-by-step explanation: