Determine whether or not the points A3 5 B 4 3 and C5 2 for

Determine whether or not the points A(3, 5), B(- 4, - 3), and C(5, 2) form a right triangle. is the triangle a right triangle? No Yes

Step 1:

distance between two points is calculated by:

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

Calculate distance between each two points:

AB = sqrt ((3 - (-4))^2 + (5 - (-3))^2) = sqrt 113

BC = sqrt ((5 - (-4))^2 + (2 - (-3))^2) = sqrt (106)

AC = sqrt ((3 - 5)^2 + (5 - 2)^2) = sqrt 13

for right angle triangle:

AB^2 = BC^2 + AC^2

But in this case above expression is not true.

AB^2 = 113

BC^2 + AC^2 = 119

So given points do not form a right angle triangle.