Question

n a right triangle, the hypotenuse has endpoints P(–3, 2) and Q(1, –3).

On a coordinate plane, line P Q has points (negative 3, 2) and (1, negative 3).

If R represents the third vertex in the triangle and R is located in the third quadrant, what is the length of PR?
3
4
5
6

Answer 1

5

Reason: For a right triangle with hypotenuse PQ, R lies on the circle with diameter PQ. Midpoint of PQ is (-1, -1/2) and radius^2 = 41/4, so R satisfies (x+1)^2+(y+1/2)^2 = 41/4. Multiplying by 4 gives 4(x+1)^2+(2y+1)^2=41. The integer solution in the third quadrant is x = -3, y = -3, so R = (-3,-3). Then PR = distance from (-3,2) to (-3,-3) = 5.