Question

Given the coordinates (9,−2) , (9,−11) , (15,−4) , and (15,−13) , what is the length of each of the two longest sides of the quadrilateral, in cm?

Answer 1

To find the length of each of the two longest sides of the quadrilateral, we first need to calculate the distance between each pair of points.

Using the distance formula:
Distance = √((x2-x1)^2 + (y2-y1)^2)

1. Between points (9, -2) and (15, -4):
Distance = √((15-9)^2 + (-4-(-2))^2)
Distance = √(6^2 + (-2)^2)
Distance = √(36 + 4)
Distance = √40
Distance ≈ 6.32 cm

2. Between points (9, -11) and (15, -13):
Distance = √((15-9)^2 + (-13-(-11))^2)
Distance = √(6^2 + (-13+11)^2)
Distance = √(36 + 2^2)
Distance = √(36 + 4)
Distance = √40
Distance ≈ 6.32 cm

3. Between points (9, -2) and (9, -11):
Distance = √(0^2 + (-11-(-2))^2)
Distance = √(0 + (-9)^2)
Distance = √(0 + 81)
Distance = √81
Distance = 9 cm

4. Between points (15, -4) and (15, -13):
Distance = √(0^2 + (-13-(-4))^2)
Distance = √(0 + (-13+4)^2)
Distance = √(0 + (-9)^2)
Distance = √81
Distance = 9 cm

Therefore, the two longest sides of the quadrilateral are 9 cm each.