Question

Given the triangle ABC with the points A = ( 4, 3 ) B = ( 1, - 5 ) C = ( 6, - 2 ) and it's dilation, triangle A'B'C', with points A' = ( 8 , 6 ) B' = ( 2, - 10 ) C' = ( 12, - 4 ) what is the scale factor?

Answer 1

The scale factor is 2.

Step-by-step explanation:

To determine the scale factor using the coordinates of each point, simply divide the respective coordinates of the new figure by the old figure.

`\begin{gathered} A^(\prime)(8,6) \\ A(4,3) \end{gathered}`
`\begin{gathered} 8/4=2 \\ 6/3=2 \end{gathered}`
`\begin{gathered} B^(\prime)(2,-10) \\ B(1,-5) \\ 2/1=2 \\ -10/-5=2 \end{gathered}`
`\begin{gathered} C^(\prime)(12,-4) \\ C(6,-2) \\ 12/6=2 \\ -4/-2=2 \end{gathered}`

As we can see above, the ratio of the coordinates of the new image triangle A'B'C and the original image triangle ABC is 2. Hence, the scale factor is 2.