Coordinate Geometry

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.

asked by Jitesh
  1. 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)

    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. Maths

    Consider the 4 points A(1,5), B(-4,6), C(0,0), D(-12,12). Find the gradients of the lines: (a) AB; (b) CD; (c) BD.
  2. maths

    Consider the 4 points A(1,5), B(-4,6), C(0,0), D(-12,12). Find the gradients of the lines: (b) CD; (c) BD.
  3. maths

    Consider the 4 points A(1,5), B(-4,6), C(0,0), D(-12,12). Find the gradients of the lines: (a) AB; (b) CD; (c) BD.
  4. maths

    Consider the 4 points A(1,5), B(-4,6), C(0,0), D(-12,12). Find the gradients of the lines: (a) AB; (b) CD; (c) BD.
  5. maths

    Consider the 4 points A(1,5), B(-4,6), C(0,0), D(-12,12). Find the gradients of the lines: (a) BD
  6. Calculus please help !

    Find the coordinates of the center of the ellipse represented by 4x^2 + 9y^2 – 18y – 27 = 0. For 2x^2 + xy + 2y^2 = 1, find , the angle of rotation about the origin, to the nearest degree. Find the distance between points at
  7. Algebra

    Find the distance between (7,0) and (-7,0) The y coordinates of the two points are the same, and the difference in x coordinates is 7 - (-7) = 14. What does that tell you about the direction and length of the line connecting the
  8. Pre-calculus HELP PLEASE !

    Find the coordinates of the center of the ellipse represented by 4x^2 + 9y^2 – 18y – 27 = 0. For 2x^2 + xy + 2y^2 = 1, find , the angle of rotation about the origin, to the nearest degree. Find the distance between points at
  9. math

    Alright, let's say you want to get from one point to another, in a 3D box. all points have an x, y and z coordinate. Point A has coordinates (25,30,5) while Point B has coordinates (50,26,18). The only given variable other than
  10. Math

    How do you find the point of intersection(s) for x = 2y2 + 3y + 1 and 2x + 3y2 = 0 A) You cannot find points of intersections for non-functions. B) Plug in 0 for x into both equations and solve for y. Then plug that answer back

More Similar Questions