Question

Δabc and Δpqr are similar. Δabc is dilated by a scale factor of 1.25 and rotated 45°Counterclockwise about point b to form Δpqr. The side lengths of Δabc are 5 units, 4.2 units, and 4 units. Match each side of Δpqr to its length.

1) 5.25 units
2) 5 units
3) 6.25 units

Answer 1

To find the lengths of the sides of Δpqr, we need to understand the effects of the dilation and rotation on the original triangle, Δabc.

Step-by-step explanation:

To find the lengths of the sides of Δpqr, we need to understand the effects of the dilation and rotation on the original triangle, Δabc.

First, let's consider the dilation. The scale factor is 1.25, which means that every length in Δabc is multiplied by 1.25 to get the corresponding length in Δpqr. So, the side lengths of Δpqr would be 5 units * 1.25 = 6.25 units, 4.2 units * 1.25 = 5.25 units, and 4 units * 1.25 = 5 units.

Next, let's consider the rotation. The triangle is rotated 45° counterclockwise about point b. This rotation does not change the lengths of the sides, so the side lengths we found earlier through dilation still apply. Therefore, the sides of Δpqr match with lengths 6.25 units, 5.25 units, and 5 units.