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1. Given the vertices of a triangle are P(3,7), Q(-8,2) and R(-4,-9). Determine the equation of the altitude that passes through the point P. 

2. The four vertices of a quadrilateral are A(-4,5), B(1,9), C(6,5) and D(1,1). What type of quadrilateral is ABCD? Use calculations to support your answer. 

3. The vertices of a kite are A(-3,1), B(0,5), C(4,2) and D(2, -9).

a. Determine the lengths of the four sides of the kite. What do you notice?

b. Determine the slopes of the diagonals (from one corner to the other corner). What do you notice?

c. Find the midpoint of the diagonal AC.

d. Find the equation of the diagonal BD.

e. Show the midpoint of AC lies on the equation of a line though BD.

f. Analyze the previous calculations and list as many properties of a kite as you can.