Question

What are the coordinates of A B C after a Dilation with a scale factor of 1/2 followed by a reflection over the x-axis

Answer 1

In general, a dilation is the outcome of applying the following transformation on a point,

`D(x,y)\to(kx,ky)`

Where k is the scale factor, this kind of dilation is about the origin, and we will use it since the problem does not specify otherwise.

In our case, the transformation is

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

Then,

`\begin{gathered} D(A)=D(-6,5)\to(-3,(5)/(2)) \\ D(B)=D(3,2)\to((3)/(2),1)_{} \\ D(C)=D(0,-1)\to(0,-(1)/(2)) \end{gathered}`

On the other hand, a reflection over the x-axis is given by the following transformation.

`(x,y)\to R_x(x,y)=(x,-y)`

Then, in our case,

`\begin{gathered} A^(\prime)=R_x(-3,(5)/(2))=(-3,-(5)/(2)) \\ B´=R_x((3)/(2),1)=((3)/(2),-1) \\ C^(\prime)=R_x(0,-(1)/(2))=(0,(1)/(2)) \end{gathered}`

Thus, the answers are

A'=(-3,-5/2)

B'=(3/2,-1)

C'=(0,1/2)