Question

Find the perimeter of the vertices a(-3,4),b(4,4)c(4,1)d(-3,1)

Answer 1

To find the perimeter, we need to sum up the lengths of all sides of the quadrilateral formed by the given vertices.

The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)² + (y2 - y1)²)

Using this formula, we can calculate the lengths of all four sides:

1. Side AB:
d(AB) = √((4 - (-3))² + (4 - 4)²)
d(AB) = √(7² + 0²)
d(AB) = √49
d(AB) = 7

2. Side BC:
d(BC) = √((4 - 4)² + (1 - 4)²)
d(BC) = √(0² + (-3)²)
d(BC) = √9
d(BC) = 3

3. Side CD:
d(CD) = √((-3 - 4)² + (1 - 1)²)
d(CD) = √((-7)² + 0²)
d(CD) = √49
d(CD) = 7

4. Side DA:
d(DA) = √((-3 - (-3))² + (1 - 4)²)
d(DA) = √(0² + (-3)²)
d(DA) = √9
d(DA) = 3

Therefore, the perimeter of the quadrilateral ABCD is:
Perimeter = AB + BC + CD + DA
Perimeter = 7 + 3 + 7 + 3
Perimeter = 20

Thus, the perimeter of the quadrilateral formed by vertices A(-3, 4), B(4, 4), C(4, 1), and D(-3, 1) is 20 units.