MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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 imageSo, 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.[tex]\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}[/tex]So, Scale Factor of Dilation = [tex]\frac{3}{4}=0.75[/tex]