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?
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.