Coordinate Geometry

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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 -

    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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