Question

Use symbols to describe the how the original figure maps to its image. (x , y) --> (___, ___)(original figure is shaded grey)

Answer 1

The transformation shown in the picture is a dilation, from the triangle TYR to the triangle T'Y'R'.

To perform a dilation each vertex was multiplied by a scale factor "k"

If the absolute value of this scale factor is less than one, |k|<1, the resulting dilation will be a reduction.

If the absolute value of the scale factor is greater than one, k|>1, the resulting dilation will be an enlargement.

In this case, the resulting figure is smaller than the original one, so the scale factor must be less than 1.

To determine the scale factor you have to divide the coordinates of the dilated shape by the coordinate of the original shape of two corresponding vertices.

Using T(6,10) and T'(3,5) you can calculate the scale factor by comparing their x-coordinates:

`\begin{gathered} k=(x_(T^(\prime)))/(x_T) \\ k=(3)/(6) \\ k=(1)/(2) \end{gathered}`

You can also compare both y-coordinates, the result will be the same since all coordinates were multiplied by the same scale factor.

So, the rule for the dilation shown on the graph is:

`(x,y)\to((1)/(2)x,(1)/(2)y)`