Question

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

Answer 1

Answer:

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

Step-by-step 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=$\sqrt{(-3-7)^2+(0-(-10))^2}$

QR=$\sqrt{(-10)^2+(10)^2}$

QR=$\sqrt{100+100}$

QR=$\sqrt{200}$--------------------------(1)

QR=14.142136

RS=$\sqrt{(9-(-3))^2+(-8-0)^2}$

RS=$\sqrt{(12)^2+(-8)^2}$

RS=$\sqrt{144+64}$

RS=$\sqrt{208}$---------------------------(2)

RS=14.422205

QS=$\sqrt{(7-9)^2+(-10-(-8))^2}$

QS=$\sqrt{(-2)^2+(-2)^2}$

QS=$\sqrt{4+4}$

QS=$\sqrt{8}$-------------------------------------(3)

QS=2.828427

According to Pythagorean Theorem,

$RS^2 = QR^ +QS^2$

Substituting the values,

$(\sqrt{208})^2 = (\sqrt{200})^2 +(\sqrt{8})^2$

$208 = 200 +8$

208 = 208

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