Erika is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She begins by assigning coordinates
to the vertices of a rectangle as shown.
Which sentence describes what Erika should do to prove that the diagonals of the rectangle are congruent?
Show that the slope of KM¯¯¯¯¯¯¯ is ba and the slope of JL¯¯¯¯¯ is −ba.
Show that the diagonals intersect at (a2, b2) .
Show that JL=KM=a2+b2−−−−−−√.
Show that JL¯¯¯¯¯ and KM¯¯¯¯¯¯¯ have the same midpoint.
Which sentence describes what Erika should do to prove that the diagonals of the rectangle are congruent?
Show that the slope of KM¯¯¯¯¯¯¯ is ba and the slope of JL¯¯¯¯¯ is −ba.
Show that the diagonals intersect at (a2, b2) .
Show that JL=KM=a2+b2−−−−−−√.
Show that JL¯¯¯¯¯ and KM¯¯¯¯¯¯¯ have the same midpoint.
2 answers:
Answer:
Option C is the right choice.
Step-by-step explanation:
The given coordinates define a rectangle, and our objective is to show that the diagonals JL and KM are congruent.
We know that rectangles possess four right angles.
To prove the congruence of the diagonals JL and KM, we will utilize the Pythagorean theorem.
In triangle KLM, KL has a length of b units while LM has a length of a units. By applying the Pythagorean theorem
In triangle JML, JM is b units long, and LM remains a units long. We again can apply the Pythagorean theorem
Thus, we find that and option C is the correct choice.
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