The coordinates of the endpoints of the hypotenuse of a right triangle are (6, 5) and (4, 3). Find the other vertex. There are two possible solutions.
A) (6, 3) or (4, 5)
B) (3, 6) or (6, 4)
C) (5, 3) or (6, 4)
D) (6, 4) or (5, 4)
E) (5, 4) or (3, 6)

Question

The coordinates of the endpoints of the hypotenuse of a right triangle are (6, 5) and (4, 3). Find the other vertex. There are two possible solutions. ​
A) (6, 3) or (4, 5)
B) (3, 6) or (6, 4)
C) (5, 3) or (6, 4)
D) (6, 4) or (5, 4)
E) (5, 4) or (3, 6)

Quizplus · Accepted Answer

First, we need to find the length of the hypotenuse using the distance formula:

sqrt((6-4)^2 + (5-3)^2) = sqrt(8)

Now, we can use this length and the Pythagorean theorem to find the possible coordinates of the other vertex:

Option 1: (6, 3)
Distance from (6, 3) to (6, 5) = 2
Distance from (6, 3) to (4, 3) = 2
sqrt(2^2 + 2^2) = sqrt(8), which matches the length of the hypotenuse

Option 2: (4, 5)
Distance from (4, 5) to (6, 5) = 2
Distance from (4, 5) to (4, 3) = 2
sqrt(2^2 + 2^2) = sqrt(8), which matches the length of the hypotenuse

Both options satisfy the conditions and are therefore possible vertices for the right triangle. The answer is choice A.

The Coordinates of the Endpoints of the Hypotenuse of a Right