Question

A quadrilateral in the coordinate plane has vertices ( -3, 1), ( 2, 1), ( 2, -2) and (-3, -2). What is the perimeter, in units, of the quadrilateral

Answer 1

To find the perimeter of the quadrilateral, we need to find the distance between its vertices and then add them up. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

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

Using this formula, we can find the distance between each pair of adjacent vertices:

Distance between (-3, 1) and (2, 1):

d = sqrt((2 - (-3))^2 + (1 - 1)^2) = sqrt(25) = 5

Distance between (2, 1) and (2, -2):

d = sqrt((2 - 2)^2 + (-2 - 1)^2) = sqrt(9) = 3

Distance between (2, -2) and (-3, -2):

d = sqrt((-3 - 2)^2 + (-2 - (-2))^2) = sqrt(25) = 5

Distance between (-3, -2) and (-3, 1):

d = sqrt((-3 - (-3))^2 + (1 - (-2))^2) = sqrt(9) = 3

Now we can add up these distances to get the perimeter:

perimeter = 5 + 3 + 5 + 3 = 16

Therefore, the perimeter of the quadrilateral is 16 units.