Question

Triangle ABC will be dilated about the point (-1, 1) by a scale factor of 2.876542BА1-8-5-4-3-2-1o12345878-1-2-3-4-5-6-7-8Identify the coordinates of the points after the transformation.A'B'C'

Answer 1

First, let us locate the coordinates of the original triangle:

A(-3, 1)

B(1, 2)

C(-2, 4)

We are given the point about which the dilation would take place as:

(-1, 1)

The rule for dilation is :

`\begin{gathered} D(x,y)\text{ }\rightarrow D^{^(\prime)}(kx,ky) \\ \text{where k is the scale factor} \end{gathered}`

The coordinates of the triangle after transformation(dilation) is:

Let us subtract the coordinates (-1,1) from each point and then multiply by the scale factor, and then add back the point (-1,1)

`\begin{gathered} A(-3,1)\rightarrow A^{^(\prime)}(-5,\text{ 1)} \\ B(1,\text{ 2) }\rightarrow B^{^(\prime)}(3,3) \\ C(-2,\text{ 4) }\rightarrow\text{ C'(}-3,7) \end{gathered}`

The plot of the original triangle and triangle after transformation is shown below:

The coordinates of the triangle after transformation is:

A'(-5,1)

B'(3,3)

C'(-3,7)