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(2)/(3)=((2\cdot3)+2)/(3)=(8)/(3) \\ \\ 1(1)/(3)=((1\cdot3)+1)/(3)=(4)/(3) \\ \\ 3(1)/(3)=((3\cdot3)+1)/(3)=(10)/(3) \end{gathered}`

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

`\begin{gathered} (-2,-(8)/(3)) \\ \\ (-4,-(4)/(3)) \\ \\ (-(10)/(3),4) \end{gathered}`

The scale factor can be found with:

`k=(NewCoordinate)/(OriginalCoordinate)`

Then, this is:

`\begin{gathered} k=(-2)/(-3)=(2)/(3) \\ \\ \end{gathered}`

You can use other coordinates to check it: