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?
The answer is 9 cm
First, we can draw the quadrilateral on a coordinate plane:
We can see that the quadrilateral is made up of two pairs of parallel lines, one pair with a length of 9 units and the other pair with a length of 11 units.
To find the length of the longest sides, we need to find the distance between points (9,-2) and (15,-4) and the distance between points (9,-11) and (15,-13).
Using the distance formula, we get:
Distance between (9,-2) and (15,-4) = $\sqrt{(15-9)^2+(-4+2)^2} = \sqrt{36+4} = \sqrt{40}$
Distance between (9,-11) and (15,-13) = $\sqrt{(15-9)^2+(-13+11)^2} = \sqrt{36+4} = \sqrt{40}$
Therefore, the length of each of the two longest sides of the quadrilateral is $\boxed{\sqrt{40}}$ cm.