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
and
is given by he formula,
![AB=√((x_2-x_1)^2+(y_2-y_1)^2)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/g9v7pwf9ks7d8dv70snpwfffdyp8834jpx.png)
Use this formula to find the length of sides.
![PQ=√((1)^2+(-4)^2) =√(17)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/pqm3m3zey5ezp8csnkbaqb2ngo1v06u8mz.png)
![QR=√((8)^2+(2)^2) =√(68)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/nj4qgyqmugn6meccredysvd0u3j64d6ufi.png)
![PR=√((9)^2+(-2)^2) =√(85)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/ahlnl3zp7vr3ybmxokdshnrjisprr4cjp5.png)
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](https://img.qammunity.org/2019/formulas/mathematics/middle-school/204p4dh3gnj6al4rv7pxuy7hj3mwg20mu5.png)
Hence, the triangle PQR is a right angle triangle.