-Let a and b represent positive real numbers. Use the right triangle with vertices at R(0,0), S(2a,0), and T(0,2b) to prove the following theorem.
"The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the
triangle."

Question

-Let a and b represent positive real numbers. Use the right triangle  with vertices at R(0,0), S(2a,0), and T(0,2b) to prove the following theorem.
"The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the
triangle."

Quizplus · Accepted Answer

The Answer is With With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

being horizontal and With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

, we have

so that

Applying the Distance Formula, we see that the distances from M to the vertices are With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

,

,
and

. That is, With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

and it follows that midpoint With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

of hypotenuse With being horizontal and being vertical, the right angle is at vertex R. Where M is the midpoint of the hypotenuse , we have so that Applying the Distance Formula, we see that the distances from M to the vertices are , , and . That is, and it follows that midpoint of hypotenuse is equidistant from vertices R, S, and T.

is equidistant from vertices R, S, and T.

-Let a and B Represent Positive Real Numbers