Saturday

March 28, 2015

March 28, 2015

Posted by **Jitesh** on Wednesday, December 19, 2012 at 1:50pm.

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 2:07pmI 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)

**Answer this Question**

**Related Questions**

Geometry - I have four questions: 1. The area of trapezoid ABCD is 60. One base ...

Geometry - The points A,B,C,D have coordinates (3,3) (8,0) (-1,1) (-6,4) ...

geometry - In rectangle ABCD, if the coordinates of A are (0, 0) and the ...

maths - the mid-point of the line FG is (6,10). if the coordinates of G is (8,14...

geometry - parallelogram ABCD has vertices A(8,2),B(6,-4),And C(-5,-4).find the...

math - Quadrilateral ABCD is a square. The coordinates of point A are (3,2), ...

maths - geometry - In a space with an orthonormal coordinate system consider the...

math - Two points P and Q have coordinates (-2, 3) and (1, 3) respectively. A ...

Geometry - The coordinates of the vertices of a parallelogram are given. Find ...

coordinate geometry - Find the value of x such that PQ=QR where the coordinates ...