Question

3. What is the perimeter of APQR with vertices P(-2, 9), Q(7, -3), and R(-2, -3) in the

Answer 1

The perimeter of APQR with vertices P(-2, 9), Q(7, -3), and R(-2, -3) in the coordinate plane is 036 units.

A perimeter is the sum of all sides of a closed figure.

The points P(-2,9) and R(-2,-3) have the same x-coordinate.

Similarly, the points Q(7,-3) and R(-2,-3) have the same y coordinate.

Therefore the line PR is perpendicular to line RQ

In other words, PRQ is a triangle that is right angled at R

Hence perimeter of the right-angled triangle = $P R+R Q+P Q$

Distance PR=$\sqrt{2-(-2)^2+9-(-3)^2} =\sqrt{144} =12$

Distance QR=$\sqrt{7-(-2)^2+(-3-(-3)^2} =\sqrt{81} =9$

Distance PQ= $\sqrt{(-2-7)^2+(9-(-3)^2} =\sqrt{225} =15$

The perimeter of the right-angled triangle is:

Perimeter of the right-angled triangle PQR =12+9+15=36

What is the perimeter?

• It is the sum of all sides of a closed figure.
• It is also defined as the total length of the boundary.

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