Q:

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

Accepted Solution

A:
The distance between two points (x₁,y₁),(x₂,y₂) = d
[tex]d = \sqrt{(x2-x1)^{2} + (y2-y1)^{2} } [/tex]

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

∴ TR = Tl
∴ Triangle TRI is isosceles.