To find the perimeter of the quadrilateral PQSR with the given coordinates of its vertices, you can use the distance formula to calculate the length of each side and then add them together.
The distance formula is:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Let's calculate the lengths of the sides:
1. Length of PQ:
PQ = √[(-1 - 0)² + (4 - 0)²] = √[1 + 16] = √17
2. Length of QR:
QR = √[(8 - (-1))² + (2 - 4)²] = √[9 + 4] = √13
3. Length of RS:
RS = √[(7 - 8)² + (6 - 2)²] = √[1 + 16] = √17
4. Length of SP:
SP = √[(0 - 7)² + (0 - 6)²] = √[49 + 36] = √85
Now, add up the lengths of all four sides to find the perimeter:
Perimeter (PQSR) = PQ + QR + RS + SP
Perimeter (PQSR) = √17 + √13 + √17 + √85
This is the exact expression for the perimeter of PQSR. If you want a numerical approximation, you can calculate the approximate value using a calculator.