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 properties of a rectangle

A rectangle has opposite - sides parallel and adjacent - sides perpendicular.

Step2: Analyze the translation property

Translation is a rigid transformation that preserves the shape and the relationships between sides (parallelism and perpendicularity). In rectangle \(JKLM\), \(JK\perp KL\), \(KL\perp LM\), \(LM\perp MJ\), and \(MJ\perp JK\). After translation to get rectangle \(J'K'L'M'\), the perpendicular relationships between adjacent sides remain the same.

Step3: Check each option

• Option A: \(\overline{J'K'}\) and \(\overline{J'M'}\) are adjacent sides of the rectangle \(J'K'L'M'\), so \(\overline{J'K'}\perp\overline{J'M'}\).
• Option B: \(\overline{J'K'}\) and \(\overline{L'M'}\) are opposite sides, so \(\overline{J'K'}\parallel\overline{L'M'}\), not perpendicular.
• Option C: \(\overline{K'L'}\) and \(\overline{J'K'}\) are adjacent sides, so \(\overline{K'L'}\perp\overline{J'K'}\), not parallel.
• Option D: \(\overline{K'L'}\) and \(\overline{L'M'}\) are adjacent sides, so \(\overline{K'L'}\perp\overline{L'M'}\), not parallel.

Answer:

A. \(\overline{J'K'}\perp\overline{J'M'}\)