Question

PLEASE HELP

Show that the triangle with vertices P(5, 6) and Q(-9, 4) and
R(-1, -2) is an isosceles right-angle triangle.

Answer 1

Explanation:

Use distance formula THREE times to find :

d P - Q d Q - R and d R - P

d^2 = ( x1-x2)^2 + (y1-y2)^2

for d P-Q :

d^2 = (5 - - 9)^2 + ( 6-4)^2 = 200

d = sqrt (200)

for d Q-R you will find d = sqrt ( 100) = 10

for d R-P you will find d = sqrt ( 100) = 10

Now we see two sides are = to 10 so it IS isosceles --------

now use Pythagorean Theorem to test for RIGHT triangle

c^2 = a^2 + b^2

(sqrt (200))^2 = 10^2 + 10^2

200 = 200 so YES it is isosceles and a RIGHT triangle