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!

Given

∆PQR points are P(-2,5), Q(-1,1), and R(7,3)

Determine whether ∆PQR is a right triangle

To proof

As given ∆PQR points are P(-2,5), Q(-1,1), and R(7,3)

First find out the sides of triangle

FORMULA

Distance formula between two points

 Distance   between two points P(-2,5) and Q(-1,1)

Distance between two points Q(-1,1)and  R(7,3)

Distance between two points  R(7,3) and P(-2,5)

now show that ∆PQR is a right triangle

Putting the value given above

85 = 17 +68

85 =85

In the right triangle

HYPOTENUSE² = BASE² + PERPENDICULAR²

This is prove above

Hence ∆PQR is a right triangle

Hence proved

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.