Answer:
The coordinates of B are (10,7).
Step-by-step explanation:
It is given that the parallelogram ABCD is the image of Parallelogram FGHI. So, B is image of G.
Since FG is parallel to x-axis therefore AB is also parallel to x-axis and the y-coordinates of A and B are same.
Let the coordinates of B be (x,7).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]FI=\sqrt{(2-4)^2+(-4-(-2))^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}[/tex]
[tex]AD=\sqrt{(-10-(-2))^2+(-1-7)^2}=\sqrt{64+64}=\sqrt{2(64)}=8\sqrt{2}[/tex]
Scale factor of dilations is the proportion of side length of image and preimage.
[tex]k=\frac{AD}{FI}=\frac{8\sqrt{2}}{2\sqrt{2}}=4[/tex]
Length of AB is 4 times length of FG. The length of FG is
[tex]FG=\sqrt{(7-4)^2+(-2-(-2))^2}=\sqrt{3^2+0}=3[/tex]
Length of AB is
[tex]AB=4\times FG=4\times 3=12[/tex]
The points are A(-2,7) and B(x,7).
[tex]AB=\sqrt{(x-(-2))^2+(7-7)^2}[/tex]
[tex]12=\sqrt{(x+2)^2}[/tex]
[tex]12=(x+2)[/tex]
[tex]x=10[/tex]
Therefore the coordinates of B are (10,7).
