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?(1 point)
___cm
The longest sides of the quadrilateral are the two diagonals.
Using the distance formula, the distance between (9,−2) and (15,−4) is:
√((15-9)^2 + (-4-(-2))^2)
= √(6^2 + (-2)^2)
= √(36 + 4)
= √40
= 2√10
Therefore, the length of one of the longest sides is 2√10 cm.
The distance between (9,−11) and (15,−13) is the same:
√((15-9)^2 + (-13-(-11))^2)
= √(6^2 + (-2)^2)
= √(36 + 4)
= √40
= 2√10
Therefore, the length of the other longest side is also 2√10 cm.
no
I apologize for the mistake.
Let's recalculate the distances between the given coordinates:
Distance between (9,−2) and (9,−11):
√((9-9)^2 + (-11-(-2))^2)
= √(0 + 9^2)
= √81
= 9
Distance between (15,−4) and (15,−13):
√((15-15)^2 + (-13-(-4))^2)
= √(0 + 9^2)
= √81
= 9
Therefore, the length of the two longest sides are 9 cm each.