SOLUTION: A triangle with vertices (3, −2), (7, 3), and (−7, 6) is what type of triangle?

Algebra.Com
Question 1030650: A triangle with vertices (3, −2), (7, 3), and (−7, 6) is what type of triangle?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!

We draw the triangle to see what it looks like:

 (3, -2), (7, 3), and (-7, 6) 



Looks suspiciously like the angle down at (3,-2) is a right
angle.   So let's see if we can prove that it is.

We find the slopes of its two sides and if that's a right angle 
then the slope of one with be the reciprocal of the other with
the opposite sign

We use the slope formula:


where (x1,y1) = (-7,6)
and where (x2,y2) = (3,-2)




We use the slope formula again:


this time with (x1,y1) = (7,3)
and where (x2,y2) = (3,-2)




Indeed  and  are reciprocals with
opposite signs, so the sides are perpendicular and
the angle with vertex (3,-2) is a right angle.

So the triangle is a right triangle.

Edwin
RELATED QUESTIONS

The three sides of a triangle are n, 4n − 2, and 4n − 7. If the perimeter of (answered by FrankM)
Heron's formula for the area of a triangle with sides a, b, c is A = the square root... (answered by lynnlo)
ΔABC has vertices at A(5,2), B(−3,1), and C(−2,5). Point D is located on (answered by mananth,ikleyn,greenestamps,MathTherapy,math_tutor2020)
In isosceles triangle ABC with side BC as the base, we are given AB = 3x − 2 and AC (answered by umail08)
Find the area of the triangle with vertices A(6,-7), B(11,-3) and... (answered by Alan3354)
What is the perimeter of triangle ABC with vertices A(-2,-2), B(2,-6), and... (answered by Alan3354)
D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m DEF? (answered by ewatrrr)
D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m... (answered by josgarithmetic)
D(5, 7), E(4, 3), and F(8, 2) form the vertices of a triangle. What is m... (answered by Fombitz)