Question

Problem 9. Find the perimeter of quadrilateral PORS with the vertices P(-2-2), Q(-1,3), R(5,3), and S(4,-2)​

Answer 1

Perimeter is 12+2√26

Explanation:

Question:

The perimeter of quadrilateral PQRS with the vertices

P(-2, -2), Q(-1, 3), R(5, 3), and S(4, -2)​

Find distances PS and QR:

Notice the y-coordinates are the same for 2 pairs of points

P(-2, -2), S(4, -2)​ and Q(-1, 3), R(5, 3)

So the distance PS = |-2|+4= 6 and QR = |-1|+5 = 6

Find the distances PQ and SR:

Use the distance formula:

`d= \sqrt{(x_(2)-x_(1) ) ^(2) + (y_(2)-y_(1) ) ^(2) }`

P(
`x_(1)` = -2,
`y_(1)` = -2), Q(
`x_(2)` = -1,
`y_(2)` = 3)

PQ =
`\sqrt{(-1--2)^(2) +(3- -2)^(2) } = \sqrt{1^(2) +5^(2) } = √(26)`

SR =
`√(26)`, because of PQ and SR are equal.

Find the perimeter of quadrilateral PQRS:

The perimeter is equal to the sum of all sides of the quadrilateral.

P= PS + QR + PQ + SR = 6+6+ √26 +√26 = 12+2√26