Question

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.

Answer 1

Answer:

Option C is the correct choice.

Step-by-step explanation:

We are given the coordinates of rectangle and we are asked to find the correct option that describes that diagonals JL and KM are congruent.

Since we that a rectangle have four right angles.

We will use Pythagorean theorem to prove that diagonals JL and KM are congruent.

In triangle KLM we can see that KL is b units long and LM is a units long. By Pythagorean theorem $\sqrt(a^{2}+b^{2})=KM$

In triangle JML we can see that JM is b units long and LM is a units long. By Pythagorean theorem $\sqrt(a^{2}+b^{2})=JL$

Therefore, we can see that $\sqrt(a^{2}+b^{2})=KM=LM$ and option C is the correct choice.  

Answer 2

I think its the last one, not to sure but I hope it helps. sorry if its wrong.