Question

the coordinates of a triangle and its image are given below. What is the scale factor?

Answer 1

In transformations, the Original figure is called "Pre-Image" and the figure after the transformation is called "Image".

In this case, you know that the coordinates of the vertices of the Pre-Image are:

$\begin{gathered} (-3,-4) \\ (-6,-2) \\ (-5,6) \end{gathered}$

Some coordinates of the Image are written as Mixed numbers. To write them as fractions you need to:

1. Multiply the whole part by the denominator of the fraction.

2. Add the product to the numerator.

3. Write the original denominator.

Then:

$\begin{gathered} 2\frac{2}{3}=\frac{(2\cdot3)+2}{3}=\frac{8}{3} \\ \\ 1\frac{1}{3}=\frac{(1\cdot3)+1}{3}=\frac{4}{3} \\ \\ 3\frac{1}{3}=\frac{(3\cdot3)+1}{3}=\frac{10}{3} \end{gathered}$

Then, the coordinates of the vertices of the Image are:

$\begin{gathered} (-2,-\frac{8}{3}) \\ \\ (-4,-\frac{4}{3}) \\ \\ (-\frac{10}{3},4) \end{gathered}$

The scale factor can be found with:

$k=\frac{NewCoordinate}{OriginalCoordinate}$

Then, this is:

$\begin{gathered} k=\frac{-2}{-3}=\frac{2}{3} \\ \\ \end{gathered}$

You can use other coordinates to check it:

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