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The coordinates of the vertices of ∆PQR are P(-2,5), Q(-1,1), and R(7,3). Determine whether ∆PQR is a right triangle. Show your work and explain your answer!

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Solution: Yes, triangle PQR is a right angle triangle.

Step-by-step explanation:

It is given that P(-2,5), Q(-1,1) and R(7,3).

Distance between two points
A(x_1,y_1) and
B(x_2,y_2) is given by he formula,


AB=√((x_2-x_1)^2+(y_2-y_1)^2)

Use this formula to find the length of sides.


PQ=√((1)^2+(-4)^2) =√(17)


QR=√((8)^2+(2)^2) =√(68)


PR=√((9)^2+(-2)^2) =√(85)

By pythagoras theorem a triangle is a right angle triangle if and only if the sum of squares of two small sides is equal to the square of the largest side.

Since the greatest side is PR.


(PQ)^2+(QR)^2=(√(17))^2+(√(68))^2 \\(PQ)^2+(QR)^2=17+68\\(PQ)^2+(QR)^2=85\\(PQ)^2+(QR)^2=(PR)^2

Hence, the triangle PQR is a right angle triangle.

User Xiong Chiamiov
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