Question

Rectangle ABCD is reflected along the y-axis and translated by $8$ inches in the upward direction to give image EFGH. If the length of AB is $12$ inches and that of FG is $8$ inches, then what is the perimeter of EFGH?

• A. $40in$
• B. $48in$
• C. $16in$
• D. $20in$

Answer 1

The correct option is A $40in$

Given: EFGH is obtained by reflection and translation of ABCD.
Since reflection and translation are rigid transformations and rigid transformations always produce congruent figures; therefore, EFGH will be congruent to ABCD.
Now, perimeter of EFGH = $2$(EF + FG) [perimeter of rectangle = $2$(length + width)]

So, we need to find the length of EF and FG to calculate the perimeter.
EF = AB (corresponding sides of congruent figures are equal)
⇒ EF = $12$ in (AB = $12$ in according to the figure)
FG = $8$ in (According to the figure)

Therefore, perimeter of EFGH = $2$(EF + FG) = $2(12+8)=2\times 20=40$ in