# Coordinate Geometry

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.

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

## 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

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