Question

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

Answer 1

To find the perimeter of the quadrilateral with the given vertices, we need to calculate the distance between each pair of consecutive vertices and then sum them up.

The distances between the points can be calculated using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

1. Distance between points A(-3, 4) and B(4, 4):
Distance AB = sqrt((4 - (-3))^2 + (4 - 4)^2)
Distance AB = sqrt(7^2 + 0^2)
Distance AB = sqrt(49)
Distance AB = 7

2. Distance between points B(4, 4) and C(-3, 4):
Distance BC = sqrt((-3 - 4)^2 + (4 - 4)^2)
Distance BC = sqrt((-7)^2 + 0^2)
Distance BC = sqrt(49)
Distance BC = 7

3. Distance between points C(-3, 4) and D(-3, 1):
Distance CD = sqrt((-3 - (-3))^2 + (1 - 4)^2)
Distance CD = sqrt(0^2 + (-3)^2)
Distance CD = sqrt(9)
Distance CD = 3

4. Distance between points D(-3, 1) and A(-3, 4):
Distance DA = sqrt((-3 - (-3))^2 + (4 - 1)^2)
Distance DA = sqrt(0^2 + 3^2)
Distance DA = sqrt(9)
Distance DA = 3

Now, we sum up all the distances to get the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 7 + 7 + 3 + 3
Perimeter = 20

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