Question

show that the point (- 2,1),(2, - 2 )and (5,2) and the vertices of a right Triangl

Answer 1

Given points are A(-2,1), B(2,-2) and C(5,2)

Let us calculate the length of each side using distance formula, we get

⇒ AB^2 = (2 + 2)^2 + (-2 - 1)^2

             = 4^2 + 3^2

             = 16 + 9

             = 25

⇒ BC^2 = (5 - 2)^2 + (2 + 2)^2

             = 3^2 + 4^2

             = 9 + 16

             = 25

⇒ AC^2 = (5 + 2)^2 + (2 - 1)^2

              = 49 + 1

              = 50.

Here, AC is the longest side.

if ABC is a right angle triangle, then

⇒ AC^2 = AB^2 + BC^2

⇒ 50 = 25 + 25

⇒ 50 = 50

Therefore, we can conclude that ABC are the vertices of right angled triangle.

Hope this helps!