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Question
Show that the points are the vertices of an isosceles right triangle.
Solution
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
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