Question

Determine whether is a right triangle for the given vertices. Explain. Q(7, –10), R(–3, 0), S(9, –8)

Answer 1

Yes, It is a right triangle for the given vertices.

Explanation:

Given:

Q(7, –10),

R(–3, 0),

S(9, –8)

To Find:

determine whether is a rig ht triangle for the given vertices = ?

Solution:

QR=
`√((-3-7)^2+(0-(-10))^2)`

QR=
`√((-10)^2+(10)^2)`

QR=
`√(100+100)`

QR=
`√(200)`--------------------------(1)

QR=14.142136

RS=
`√((9-(-3))^2+(-8-0)^2)`

RS=
`√((12)^2+(-8)^2)`

RS=
`√(144+64)`

RS=
`√(208)`---------------------------(2)

RS=14.422205

QS=
`√((7-9)^2+(-10-(-8))^2)`

QS=
`√((-2)^2+(-2)^2)`

QS=
`√(4+4)`

QS=
`√(8)`-------------------------------------(3)

QS=2.828427

According to Pythagorean Theorem,

`RS^2 = QR^ +QS^2`

Substituting the values,

`(√(208))^2 = (√(200))^2 +(√(8))^2`

`208 = 200 +8`

208 = 208

Pythagorean theorem is satisfied. Hence it is a right triangle.