Finding Side Lengths
2 in.
xin.
These two figures are the image and pre-image of a
dilation
Find the lengths of the missing sides.
4 in.
5 in.

Step-by-step explanation:

As the two figure are the image and pre-image of a dilation.

Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.

As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.

It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in

Lets determine the missing side of the right side triangle by the same rule.

As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5

So, the value of x will be 2.5

Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.

so

y + 1 = 2(3)         ∵ 3 in (image side) is multiplied by 2

y + 1 = 6

y = 6 - 1

y = 5

So, the value of y = 5

Therefore,