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 = (0-3)/(8-3) = -3/5

m CD = (4-1)/(-6+1) = -35

so AB and CD are parallel (same slope)

if DA and CB are also parallel, it is a parallelogram

m DA = (4-3)/(-6-3) = -1/9

m CB = (0-1)/(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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