Question

Prove that the triangle with vertices P(-4,0), Q(3,5), and R(8,-2) is a right triangle.

Answer 1

Answer:

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Step-by-step explanation:

PR=9+4+36−−−−−−−−√=7

PQ=36+9+4−−−−−−−−√=7

RQ=1+25+64−−−−−−−−−√=98−−√

PQ2+RQ2=49+49=98

Answer 2

As the triangle satisfies the Pythagoras's theorem, it is a right angled triangle.

What is Pythagoras Theorem?

According to Pythagoras Theorem, in a right angled triangle the square of the side opposite to the right angle is equal to the sum of squares of the other two sides.

Height² + Base² = Hypotenuse²

For a triangle to be a right triangle, it should satisfy Pythagoras's Theorem.

The length of the sides of the triangle will be determined using Distance formula.

PQ² = ( 3 - (-4))² + (5-0)²

PQ² = 49 + 25

PQ² = 74

QR² = ( 8 - 3)² + (-2-5)²

QR² = 25 + 49

QR² = 74

RP² = (-4 - 8)² + ( 0 +2)²

RP² = 144+4

RP² = 148

Now checking for Pythagoras theorem,

148 = 74 +74

148  = 148

RP² = PQ²+QR²

To know more about Pythagoras Theorem

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