Find the perimeter of PQR with vertices P(-2, 9), Q(7, -3), and

R(-2, -3).

To find the perimeter of triangle PQR with vertices P(-2, 9), Q(7, -3), and R(-2, -3), we need to find the lengths of all three sides and then add them together.

The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

Now let's find the lengths of the three sides:

1. Length of PQ:
P(-2, 9) and Q(7, -3)

d(PQ) = √((7 - (-2))² + (-3 - 9)²)
= √((7 + 2)² + (-3 - 9)²)
= √(9² + (-12)²)
= √(81 + 144)
= √225
= 15

2. Length of QR:
Q(7, -3) and R(-2, -3)

d(QR) = √((-2 - 7)² + (-3 - (-3))²)
= √((-2 - 7)² + (-3 + 3)²)
= √((-9)² + 0²)
= √(81 + 0)
= √81
= 9

3. Length of RP:
R(-2, -3) and P(-2, 9)

d(RP) = √((-2 - (-2))² + (9 - (-3))²)
= √((-2 + 2)² + (9 + 3)²)
= √(0² + 12²)
= √(0 + 144)
= √144
= 12

Finally, we can find the perimeter by adding the lengths of all three sides:

Perimeter = PQ + QR + RP
= 15 + 9 + 12
= 36

Therefore, the perimeter of triangle PQR is 36 units.

To find the perimeter of a triangle, we need to calculate the lengths of all three sides and then sum them up.

Let's calculate the lengths of the sides of triangle PQR using the distance formula.

1. Side PQ:
- Coordinates of P: (-2, 9)
- Coordinates of Q: (7, -3)

The distance formula is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values, we have:
distance PQ = √((7 - (-2))^2 + (-3 - 9)^2)
= √(9^2 + (-12)^2)
= √(81 + 144)
= √(225)
= 15

2. Side QR:
- Coordinates of Q: (7, -3)
- Coordinates of R: (-2, -3)

Using the distance formula:
distance QR = √((-2 - 7)^2 + (-3 - (-3))^2)
= √((-9)^2 + 0^2)
= √(81 + 0)
= √(81)
= 9

3. Side RP:
- Coordinates of R: (-2, -3)
- Coordinates of P: (-2, 9)

Using the distance formula:
distance RP = √((-2 - (-2))^2 + (-3 - 9)^2)
= √((0)^2 + (-12)^2)
= √(0 + 144)
= √(144)
= 12

Now, we can sum up the lengths of all three sides to find the perimeter of triangle PQR:
Perimeter = PQ + QR + RP
= 15 + 9 + 12
= 36

Therefore, the perimeter of triangle PQR is 36 units.

36

just use the distance formula for each side, then add them up. For example,

QR = √[(-2-7)^2 + (-3 - -3)^2] = 9