SOLUTION: Analytic Geometry 1.a) Draw the triangle with vertices P(-2,-2), Q(2,4), and R(8,0). b) Show algebraically that PQR is a right triangle. c) Is PQR also an isosceles triangle?

Question 177793: Analytic Geometry
1.a) Draw the triangle with vertices P(-2,-2), Q(2,4), and R(8,0).
b) Show algebraically that PQR is a right triangle.
c) Is PQR also an isosceles triangle?
Use algebraic reasoning to justify your answer.

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
a.)
.
.
.
b.) You can use the Pythagoran theorem to check if PQR is a right triangle.

Using the distance formula to calculate line segment lengths,

.
.
.

Since the two sides are equal, the Pythagorean theorem holds and PQR is a right triangle.
.
.
.
c.) The legs of an isoceles triangle are congruent.
Since , then so this right triangle is also an isoceles triangle.

RELATED QUESTIONS
Analytic Geometry 13.a) Draw a triangle with vertices P(-2, -2), Q(2, 4), and R(8, 0).... (answered by vleith)

Analytic Geometry 13. a) Draw the triangle with vertices P(-2,-2),Q(2,4), and R(8,0). (answered by solver91311)

Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4).... (answered by josgarithmetic)

Use 2 methods to show triangle with vertices A (-6, 5), B (2, 1), C (-2, -6) is a right... (answered by Alan3354)

The coordinates of the vertices of ∆PQR are P (0,5), Q (5,0), and R (10,5).... (answered by mananth)

Use coordinate geometry to prove that triangle PQR is isosceles... ^ | |---------Q... (answered by hovuquocan1997)

find the perimeter of the polygon PQR with it vertices at P(-4, 1), Q(2, 1), and R(0,... (answered by josgarithmetic)

The coordinates of the vertices of ∆PQR are P (0,4), Q (4,0), and R (8,4) Determine... (answered by Alan3354,josgarithmetic)