Question

Prove taht the points (-2 , 1) , (-1 , 4) and (0 , 3) are the vertices of a right - angled triangle.

Answer 1

AB = `sqrt ((-2-0)^2 + (1-3)^2) = sqrt (4 + 4) = sqrt 8` units

BC = `sqrt ((10 + 1)^2 + (3 - 4)^2) = sqrt ( 1 + 1) = sqrt 2` units

AC = `sqrt ((-2 + 1)^2 + (1 - 4)^2) = sqrt (1 + 9) = sqrt 10` units

AB²+ BC² = 8 + 2 = 10

AC² = 10

∵ AB²+ BC² = AC² 

∴ A , B and C are the verices of a right angled triangle.