Question

Triangle ABCTriangle ABC ​is transformed with the center of dilation at the origin. Pre-image: △ABC with vertices A(−5, −4), B(−7, 3), C(3, −2) Image: △A′B′C′ with vertices A′(−3.75, −3), B′(−5.25, 2.25), C′(2.25, −1.5) What is the scale factor of the dilation that maps the pre-image to the image?

Answer 1

Pre Image  having vertices : △ABC with vertices A(−5, −4), B(−7, 3), C(3, −2)

Image having vertices : △A′B′C′ with vertices A′(−3.75, −3), B′(−5.25, 2.25), C′(2.25, −1.5).

As, Size of Preimage > Size of image

So, 0<Dilation Factor <1

When a triangle is dilated , the preimage and image are similar to each other .

Scale factor can be get through by finding the ratio of any of corresponding sides of triangle.

$\frac{A'B'}{AB}=\frac{\sqrt{2.25 +27.5625}}{\sqrt{4+49}}=\sqrt{\frac{29.8125}{53}}=\sqrt{0.5625}=0.75=\frac{3}{4}$

So, Scale Factor of Dilation = $\frac{3}{4}=0.75$