Question

3
rectangle abcd translates 4 units down and 2 units to the right to form rectangle abcd. the vertices of rectangle abcd are labeled in alphabetical
order going clockwise around the figure. if ab = 3 units and ad = 5 units, what is the length of bc?
a. 11 units
b. 5 units
c. 9 units
d. 3 units

Explanation:

Step1: Recall the property of translation

Translation is a rigid transformation. It means that the shape and size of the figure do not change. So, rectangle \(A'B'C'D'\) is congruent to rectangle \(ABCD\).

Step2: Identify the corresponding sides

In rectangle \(ABCD\), \(BC = AD\) (opposite sides of a rectangle are equal). Since \(AD = 5\) units, \(BC=5\) units.
Because of the congruence of \(ABCD\) and \(A'B'C'D'\) (due to translation), \(B'C'=BC\)

Answer:

B. 5 units