Question

Prove that a triangle with coordinates

A(5, 6), B(8,5), and C(2, -3) is a right triangle.

Answer 1

Because the side of the triangle forms pythagoras tripple

Line AB = √10

Line BC = 10

Line AC = √90

Explanation:

From the question,

In the triangle,

Line AB = √[(8-5)²+(5-6)²]

Line AB = √(3²+-1²)

Line AB = √(9+1)

Line AB = √10

Also,

Line BC = √[(2-8)²+(-3-5)²]

Line BC = √(-6²+(-8)²)

Line BC = √(36+64)

Line BC = √100

Line BC = 10 unit.

Finally,

Line AC = √[(5-2)²+(6+3)²]

Line AC = √(3²+9²)

Line AC = √(9+81)

Line AC = √90.

From the above length of the line in the triangle,

Line AC, Line BC and Line AC are pythagoras triple.

I.e

10² = (√10)²+(√90)²

100 = 10+90

100 = 100.

Note only a a right angle triangle obeys pythagoras theorem.