Question

Given the triangle ABC with the points A = ( 4, 6 ) B = ( 2, 8 ) C = ( 5, 10 ) and it's dilation, triangle A'B'C', with points A' = ( 8, 12 ) B' = ( 4, 16 ) C' = ( 10, 20 ) what is the scale factor?

Answer 1

Solution:

Given the triangle ABC with the points below

$A=(4,6),\text{ }B=(2,8)\text{ and }C=(5,10)$

And it's dilation, triangle A'B'C, with points

$A^{\prime}=(8,12),\text{ }B^{\prime}=(4,16)\text{ and }C^{\prime}=(10,20)$

To find the scale factor of dilation, the formula is

Scale factor = Dimension of the new shape ÷ Dimension of the original shape, i.e.

$Scale\text{ factor}=\frac{Dimensio\text{n of the new point}}{Dimension\text{ of the original point}}$

Taking point A and A',

Substituting their dimensions into the scale factor formula

$\begin{gathered} Scale\text{ factor}=\frac{(8,12)}{(4,6)}=\frac{2(4,6)}{(4,6)}=\frac{2}{1}=2 \\ Scale\text{ factor}=2 \end{gathered}$

Hence, the scale factor is 2