Question

Triangle PQR has vertices at the following coordinates : P(0,1) Q(3,2) R(5,-4) . Determine wether or not triangle PQR is a right triangle . Show all calculations for full credit .

Answer 1

Here is my answer. Hope this help.

Answer 2

The sum of the squares of two sides is not equal to the square of the third side, the triangle PQR is not a right 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

If a triangle is a right angle, then its sides should satisfy Pythagoras theorem.

The distance formula will be used to determine the length of the sides.

PQ² =  ( 3 - 0)² + (2-1)²

PQ² = 10

PQ = √10

RQ² =  ( 5 - 3)² + (-4-2)²

RQ² = 40

RQ = √40

RP² =  ( 5 - 0)² + (-4-1)²

RQ² =  25 + 36

RQ² =  61

Applying the Pythagoras's Theorem,

61 ≠ 40 + 10

Therefore, it is not a right angled triangle.

To know more about Pythagoras Theorem

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