Question

Dilation(x,y)(3/4x,3/4) reflection:in the X-axis

Answer 1

Step-by-step explanation:

To know the new coordinates for F', G', and H', we need to follow the rule, so:

`\begin{gathered} (x,y)_{}\to((3)/(4)x,(3)/(4)y) \\ F(-2,2)\to((3)/(4)\cdot-2,(3)/(4)\cdot2)=F^(\prime)((-3)/(2),(3)/(2)) \\ G(-2,-4)\to((3)/(4)\cdot-2,(3)/(4)\cdot-4)=G^(\prime)((-3)/(2),-3) \\ H(-4,-4)\to((3)/(4)\cdot-4,(3)/(4)\cdot-4)=H^(\prime)(-3,-3) \end{gathered}`

Then, to reflect over the x-axis, we need to use the following rule:

(x, y) ---> (x, -y)

So, the new coordinates F'', G'', and H" after the reflection are:

F'(-3/2, 3/2) ----> F"(-3/2, -3/2)

G'(-3/2, -3) -----> G"(-3/2, 3)

H'(-3, -3) --------> H"(-3, 3)

Therefore, the graph of figure F"G"H" is: