Question

The vertices of a triangle are A (-2,-5), B(-2,6) and C (9,-5). The vertices of triangle A'B'C' obtained by dilating triangleABC from the origin areA'(-8, -20). B'(-8, 24) and C (36, -20).What is the scale factor?

Answer 1

The vertices of traingle ABC are :

A (-2,-5),

B (-2,6)

C (9,-5)

Scale Factor : It is the ratio of the measurements of original size to the new size.

`\text{ Sacle Factor = }\frac{New\text{ measurement }}{Origi\text{ nal measurement}}`

The coordinates of the new triangle A'B'C' is :

A'(-8, -20).

B'(-8, 24)

C' (36, -20).

Ratio of the coordinates are :

`\text{ Scale Factor = }(A^(\prime))/(A)=(B^(\prime))/(B)=(C^(\prime))/(C)`

Substitute the value and simplify :

`\begin{gathered} \text{ Scale Factor = }(A^(\prime))/(A)=(B^(\prime))/(B)=(C^(\prime))/(C) \\ \text{ Scale Factor = }((-8,-20))/((-2,-5))=((-8,24))/((-2,6))=((36,-20))/((9,-5)) \\ \text{Scale Factor = }(4(-2,-5))/((-2,-5))=(4(-2,6))/((-2,6))=(4(9,-5))/((9,-5)) \\ Scale\text{ Factor = 4} \end{gathered}`

Scale Factor is 4.

Answer : Scale Factor is 4.