Polygons in the Coordinate Plane Practice 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 can calculate the distance between each pair of points.

1. Distance between (9,−2) and (9,−11):
d = √[(9-9)^2 + (-2 - (-11))^2]
d = √[0 + 81]
d = √81
d = 9 cm

2. Distance between (9,−11) and (15,−13):
d = √[(15-9)^2 + (-13 - (-11))^2]
d = √[36 + 4]
d = √40
d ≈ 6.32 cm

3. Distance between (15,−13) and (15,−4):
d = √[(15-15)^2 + (-13 - (-4))^2]
d = √[0 + 81]
d = √81
d = 9 cm

4. Distance between (15,−4) and (9,−2):
d = √[(9-15)^2 + (-2 - (-4))^2]
d = √[36 + 4]
d = √40
d ≈ 6.32 cm

The two longest sides of the quadrilateral are 9 cm and 9 cm.