Question

The coordinates of the vertices of VPQR are P(-2,5), Q(-1,1), and R(7,3). Determine whether VPQR is a right triangle. Show your work? Need help solving

The coordinates of the vertices of `DeltaPQR" are "P(-2,5), Q(-1,1), and R(7,3).` Determine whether `DeltaPQR` is a right triangle. Show your work? Need help solving

Answer 1

`DeltaPQR` is right-angled at `Q.`

Explanation:

Using the Distance Formula, we have,

`PQ^2=(-2-(-1))^2+(5-1)^2=1+16=17.`

`QR^2=(-1-7)^2+(1-3)^2=64+4=68.`

`RP^2=(7-(-2))^2+(3-5)^2=81+4=85.`

`:. PQ^2+QR^2=17+68=85=RP^2.`

Therefore, by the Converse of Pythagoras Theorem, `DeltaPQR`

is right-angled at `Q.`