SOLUTION: Analytic Geometry 13.a) Draw a 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 trianlge?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Analytic Geometry 13.a) Draw a 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 trianlge?       Log On


   

Question 200409: Analytic Geometry
13.a) Draw a 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 trianlge? Use algebraic reasoning to justify yopur answer.
Can you please help me with this question and thankss alott?!#@##
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
find the length between each of the three sets of two points
Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%28-2-2%29%5E2+%2B+%28-2-4%29%5E2%29=+7.21110255092798+


For more on this concept, refer to Distance formula.

Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%28-2-8%29%5E2+%2B+%28-2-0%29%5E2%29=+10.1980390271856+


For more on this concept, refer to Distance formula.

Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%288-2%29%5E2+%2B+%280-4%29%5E2%29=+7.21110255092798+


For more on this concept, refer to Distance formula.


Now use Pathogrean theorem. If c%5E2+=+a%5E2+%2B+b%5E2 then it is a right triangle
If two side are the same length, then it is isocelese