Posted by Jitesh on Wednesday, December 19, 2012 at 1:50pm.
Please help!!!!!
The points A,B,C,D have coordinates (3,3), (8,0), (1,1), (6,4) respectively.
a) Find the gradients of the lines AB and CD
b) Show that ABCD is a parallelogram
c) Find the coordinates of the point of intersection of the diagnols AC and BD.
Please help me by showing all methods of working out answer.

Coordinate Geometry  Damon, Wednesday, December 19, 2012 at 2:07pm
I assume that by gradient you mean slope, m
m AB = (03)/(83) = 3/5
m CD = (41)/(6+1) = 35
so AB and CD are parallel (same slope)
if DA and CB are also parallel, it is a parallelogram
m DA = (43)/(63) = 1/9
m CB = (01)/(8+1) = 1/9
sure enough, parallelogram
where is the middle?
halfway between A and C (or D and B)
do A and C
average x = (1 + 3)/2 = 1
average y = (1+3)/2 = 2
so (1,2)
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