Question

Locate the images A B C or the points A B and c under this dilation

Answer 1

The Solution:

The coordinates of points A, B and C are

`\begin{gathered} A(3,6) \\ B(6,7) \\ C(9,8) \\ P(4,8) \end{gathered}`

We are required to locate the images A', B', and C'

The difference between point A and its center of dilation, P, is

`\begin{gathered} P-A=(4,8)-(3,6)=(4-3,8-6)=(1,2) \\ \text{Applying a dilation of scale factor of 2, we get} \\ 2*(1,2)=(2,4) \\ So,\text{ the coordinate of A' is} \\ A^(\prime)=(4,8)+(1,2)=(4+1,8+2)=(5,10) \end{gathered}`

The difference between point B and its center of dilation, P, is

`\begin{gathered} P-B=(4,8)-(6,7)=(4-6,8-7)=(-2,1) \\ \text{Applying a dilation of scale factor of 2, we get} \\ 2*(-2,1)=(-4,2) \\ So,\text{ the coordinate of B' is} \\ B^(\prime)=(4,8)+(-4,2)=(4+-4,8+2)=(0,10) \end{gathered}`

The difference between point C and its center of dilation, P, is

`\begin{gathered} P-C=(4,8)-(9,8)=(4-9,8-8)=(-5,0) \\ \text{Applying a dilation of scale factor of 2, we get} \\ 2*(-5,0)=(-10,0) \\ So,\text{ the coordinate of B' is} \\ B^(\prime)=(4,8)+(-10,0)=(4+-10,8+0)=(-6,8) \\ \\ \text{Therefore, the required images are:} \\ A^(\prime)=(5,10) \\ B^(\prime)=(0,10) \\ C^(\prime)=(-6,8) \end{gathered}`