Question

Marcus drew rectangle EFGH. Then, he drew a translation of it using the rule (x, y - 16) to create rectangle E'F'G'H'. Line segment GH is 5 inches. How long is line segment G' H'

Answer 1

Step-by-step explanation: To find the length of line segment G'H', we need to use the same ratio as the original rectangle. Let's call the length of side EF equal to x. Then, we know that EF = x and FG = 16 + x.

Using similar triangles, we can set up an equation for G'H':

(x/5) * (5 - 16)/(16 + x) = G'H'/EF'

Simplifying this equation, we get:

(x/5) * (-7/16 + x/16) = G'H'/EF'

Multiplying both sides by EF'/G'H', we get:

(x/5) * (-7/16 + x/16) * (EF'/G'H') = 3/2

Substituting this into our equation, we get:

(x/5) * (-7/16 + x/16) * 3/2 = G'H'/EF'

Simplifying further, we get:

(x/5) * (-7/16 + x/16) * 3/2 = 3/2

Expanding and simplifying, we get:

Multiplying through by 8/5, we get:

(-7/16 + x/16) * (-7/16 + x/16) * 12/5 = 0

Simplifying further, we get:

-7/16 + x/16 = 0

Adding x to both sides, we get:

x = 7/16

Therefore, the length of line segment G'H' is 7/16 inches.