Question

Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park:

Answer 1

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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$FI=\sqrt{(2-4)^2+(-4-(-2))^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}$

$AD=\sqrt{(-10-(-2))^2+(-1-7)^2}=\sqrt{64+64}=\sqrt{2(64)}=8\sqrt{2}$

Scale factor of dilations is the proportion of side length of image and preimage.

$k=\frac{AD}{FI}=\frac{8\sqrt{2}}{2\sqrt{2}}=4$

Length of AB is 4 times length of FG. The length of FG is

$FG=\sqrt{(7-4)^2+(-2-(-2))^2}=\sqrt{3^2+0}=3$

Length of AB is

$AB=4\times FG=4\times 3=12$

The points are A(-2,7) and B(x,7).

$AB=\sqrt{(x-(-2))^2+(7-7)^2}$

$12=\sqrt{(x+2)^2}$

$12=(x+2)$

$x=10$

Therefore the coordinates of B are (10,7).