Question

rectangle jklm is graphed on the coordinate plane shown below. rectangle jklm will be translated 5 units right and 2 units up to produce rectangle jklm. which statement about the line segments of rectangle jklm is true? a jk⊥jm b jk∥lm c kl∥jk d kl⊥lm

Explanation:

Step1: Recall translation property

Translation is a rigid - motion transformation. It preserves the shape, size, and orientation of the figure. So, parallel lines in the original rectangle remain parallel in the translated rectangle.
In rectangle JKLM, JK is parallel to LM and KL is parallel to JM. After translation 5 units right and 2 units up to get rectangle J'K'L'M', the parallel relationships are maintained.

Step2: Analyze options

• Option A: J'K' and J'M' are adjacent sides of the rectangle, so they are perpendicular, not parallel.
• Option B: J'K' and L'M' are opposite sides of the rectangle. In a rectangle, opposite sides are parallel. Since translation preserves parallelism, J'K' || L'M'.
• Option C: K'L' and J'K' are adjacent sides of the rectangle, so they are perpendicular, not parallel.
• Option D: K'L' and L'M' are adjacent sides of the rectangle, so they are perpendicular, not parallel.

Answer:

B. J'K' || L'M'