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olganol [36]
3 years ago
14

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

Mathematics
1 answer:
andriy [413]3 years ago
8 0

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.

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