Question

triangle TRI has vertices T(15,6),R(5,1),and I(5,11).Use coordinate geometry to prove that triangle TRI is isosceles

Answer 1

The distance between two points (x₁,y₁),(x₂,y₂) = d

`d = \sqrt{(x2-x1)^(2) + (y2-y1)^(2) }`

T(15,6),R(5,1),and I(5,11)
The distance between T,R =TR
TR =
`\sqrt{(5-15)^(2) + (1-6)^(2) }` = 5√5
The distance between l,R = lR
lR =
`\sqrt{(5-5)^(2) + (1-11)^(2) }` = 10
The distance between T,l = Tl
Tl =
`\sqrt{(5-15)^(2) + (11-6)^(2) }` = 5√5

∴ TR = Tl
∴ Triangle TRI is isosceles.