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

3/4

Explanation:

Answer 2

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.

`(A'B')/(AB)=(√(2.25 +27.5625))/(√(4+49))=\sqrt{(29.8125)/(53)}=√(0.5625)=0.75=(3)/(4)`

So, Scale Factor of Dilation =
`(3)/(4)=0.75`