"Draw the triangle w/ the given vertices and show that the triangle is a right triangle A9-1,1), B(6,-2) and C (4,3)

Question

"Draw the triangle w/ the given vertices and show that the triangle is a right triangle A9-1,1), B(6,-2) and C (4,3)

Answer 1

First, plot the points on a coordinate system and connect them so that you get a triangular shape.   Then find the side lengths of the triangle using the distance formula:

 

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

 

 

You will need to use this formula three times.

 

Then use the Pythagorean theorem.  If the sum of the squares of the 2 shorter sides equals the square of the longest side, then you have a right triangle.

Answer 2

The slopes of the three line segments are:       (y₂-y₁)/(x₂-x₁)

 

    AB:      ((-2) - 1) / (6 - (-1)) = -3/7

    BC:      (3 - (-2)) / (4 - 6) = -5/2

    CA:      (1 - 3)/((-1) - 4) = 2/5

 

Line segments BC and CA are perpendicular (slopes are negative reciprocals); thus, this is a right triangle.