SOLUTION: Analytic Geometry
13. 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
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13. 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
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Question 199383: Analytic Geometry
13. 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 anser.
Use the formula for the slope of a line passing through two points, namely:
Where and are the two points. Do this twice: once for segment PQ and once for segment QR.
Since:
If
then
and PQR is a right triangle by definition.
The triangle is isosceles if the measure of PQ is equal to the measure of QR. Use the distance formula,
where and are the coordinates of the endpoints of the segment to calculate the measures of PQ and QR. If they are equal, the triangle is isosceles; otherwise not.
