Question

Show that the points A(3, 0), B(6, 4) and C(–1, 3) are the vertices of an isosceles right triangle.

Answer 1

The given points are A (3, 0), B(6, 4) and C(-1, 3) Now,

`AB = sqrt((3-6)^2 +(0-4)^2 ) = sqrt((-3)^2 +(-4)^2)`

`= sqrt((9+16)) = sqrt(25) = 5`

`BC = sqrt((6+10)^2 +(4-3)^2 )= sqrt((7)^2+(1)^2)`

`=sqrt(49+1) = sqrt(50) = 5 sqrt(2)`

`AC = sqrt((3+1)^2 +(0-3)^2) = sqrt((4)^2 + (-3)^2)`

`= sqrt(16+9) = sqrt(25) =5`

`∵AB +AC and AB^2 +AC^2 = BC^2`

Therefore,A (3, 0), B(6, 4) and C(-1, 3)  are die vertices of an isosceles right triangle