Answer:
See below.
Step-by-step explanation:
a)
Slopes of three sides:
m(PQ) = (-1 + 4)/(2 + 2) = 3/4
m(QR) = (-1 + 9)/(2 - 8) = 8/(-6) = -4/3
m(PR) = (-4 + 9)/(-2 - 8) = 5/(-10) = -1/2
Since the slopes of PQ and QR are negative reciprocals, sides PQ and QR are perpendicular.
b)
The triangle is a a right triangle, and angle Q is a right angle.
Side PR is opposite angle Q, so side PR is the hypotenuse.
In a right triangle, the hypotenuse is always longer than the legs.
In a right triangle, the legs may be congruent.
For the triangle to be isosceles, the legs would have to be congruent.
The legs are sides PQ and QR.
length(PQ) = √[(-4)² + (-3)²] = 5
length(QR) = √[(6)² + (-8)²) = 10
Since the lengths of the legs are not equal, the triangle is not isosceles.
