Question

How to determine if a triangle is a right triangle with coordinates?

Answer 1

The answer in the procedure

Explanation:

step 1

Find the length sides of the triangle

Given the coordinates

A(a1,a2), B(b1,b2) and C(c1,c2)

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

so

Calculate

dAB,dBC and dAC

substitute in the formula

`dAB=\sqrt{(b2-a2)^(2)+(b1-a1)^(2)}`

`dBC=\sqrt{(c2-b2)^(2)+(c1-c1)^(2)}`

`dAC=\sqrt{(c2-a2)^(2)+(c1-a1)^(2)}`

step 2

Apply Pythagoras theorem

`c^(2)=a^(2)+b^(2)`

where

c is the greater side

a and b are the other two sides

substitute the distances in the equation

If the equation is true

therefore

Its a right triangle