Math homework question?

Question

Could you help me out with this? Either tell me the answer, or help me get through it?

2. The vertices of a parallelogram are T (2,2), H (12,2), A (16,8) and M (6,8).

a. Plot and connect the points on a grid.
b. Draw in the diagonals for the parallelogram.
c. Find the length of each diogonal.
d. Find the coordinates of the poit of intersection of the diagonals.

3. A polie investigator can determine if a car was speeding before an accident by measuring the skid marks. The formula s= 2 [insert square root symbol here..that weird check mark looking thing] 5l, where s represents speed measured in miles per hour, and l represents the length of the skid marks measured in feet will determine if a car was speeding. The officer measured the skid marks left by a car to be approximately 120 ft. The driver of the car claims that she was not exceeding the 40-mph speed lmit. Is she telling the truth? Explain. How long would have the skid marks measured if she had been driving

the speed limit?

Answer 1

I hope you can plot the points yourself; there's not much I can help you with here except to note the obvious: that (12, 2), for instance, means you go 12 units to the right and 2 units up from the origin.
c) The diagonals are:
TA = (16-2, 8-2) = (14, 6) with length √(14^2 + 6^2) = 2√(7^2 + 3^2) = 2√(58)
HM = (6-12, 8-2) = (-6, 6) with length √(6^2 + 6^2) = 6√2.
d) The diagonals of a parallelogram bisect each other, so we can take the midpoint of TA or of HM to get (9, 5) as the intersection point.

3). s = 2√(5l)
We have l ≈ 120 ft, so s ≈ 2√600 = 20√6 = 49 mph. So the driver of the car does not appear to be telling the truth.
If she had been going 40 mph we would have
40 = 2√(5l)
=> √(5l) = 20
=> 5l = 400
=> l = 80 ft.