To find the perimeter of triangle PQR with the given vertices, we first need to calculate the lengths of all three sides: PQ, QR, and RP.
1. **Calculating PQ:**
Using the distance formula, which is given by d = √((x2 – x1)² + (y2 – y1)²), we plug in the coordinates of P(2, 9) and Q(7, 3):
PQ = √((7 – 2)² + (3 – 9)²)
= √(5² + (-6)²)
= √(25 + 36)
= √61
2. **Calculating QR:**
Now, we calculate the distance between Q(7, 3) and R(2, 3):
QR = √((2 – 7)² + (3 – 3)²)
= √((-5)² + 0²)
= √25
= 5
3. **Calculating RP:**
Finally, we find the distance between R(2, 3) and P(2, 9):
RP = √((2 – 2)² + (9 – 3)²)
= √(0² + 6²)
= √36
= 6
4. **Calculating the Perimeter:**
Now, we sum the lengths of all sides to get the perimeter:
Perimeter = PQ + QR + RP
= √61 + 5 + 6
= √61 + 11
Thus, the perimeter of triangle PQR is approximately 22.81 units when you calculate √61.