Coordinate Geometry
posted by Jitesh
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.

Damon
I assume that by gradient you mean slope, m
m AB = (03)/(83) = 3/5
m CD = (41)/(6+1) = 35
so AB and CD are parallel (same slope)
if DA and CB are also parallel, it is a parallelogram
m DA = (43)/(63) = 1/9
m CB = (01)/(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)
Respond to this Question
Similar Questions

maths
the midpoint of the line FG is (6,10). if the coordinates of G is (8,14) find the coordinates of F. There are a number of ways to solve this but I think the simplest is to use the definiton of midpoint. We know mdpt(FG) = 1/2(F+G) … 
Mathematics
In an orthonormal system, you're given the following: Point P(1,2) Lina a=cartesian eqn:4x3y+6=0 Line b=parametric eqns:x=5+3& y=& (real n°) Circle z=cartesian eqn:x²+y²2x3=0 (a)Calculate the angle between lines a an b (b)Calculate … 
maths  geometry
In a space with an orthonormal coordinate system consider the plane; &: 4x3y=12 (a)(i)Find the coordinates of the points of intersection of the plane & with the coordinates axes (=axes intersections? 
math
Quadrilateral ABCD is a square. The coordinates of point A are (3,2), coordinates of point B are (3,2),and the coordinates of points C are (3,4). where on a coordinate plane would I mark the location of point D? 
Geometry
1) find the coordinate of the image of point (1,2) translated left 2 units and reflected over the x axis 2) Find the coordinate of the image of the point (2, 4) reflected over the xaxis 3) Determine the midpoint of the segment whose … 
Geometry
The points A,B,C,D have coordinates (3,3) (8,0) (1,1) (6,4) respectively. Find the coordinates of the point of intersection of the diagonals AC and BD? 
Geometry
I have four questions: 1. The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid. 2. In trapezoid ABCD, line BC is parallel … 
math
Two points P and Q have coordinates (2, 3) and (1, 3) respectively. A translation map point P to P’ (10, 10) (a) Find the coordinates of Q’ the image of Q under the translation (b) The position vector of P and Q in (a) above are … 
Precalc
HI, can someone can please help me find the coordinates of the two halfway points of the principal cycles. Here are some answers that might help. I found the interval: (0,pi/2) The equation of the left vertical asymptote: x=0, and … 
Reposting question Precalc
HI, Function: y=5cot(2x) can someone can please help me find the coordinates of the two halfway points of the principal cycles. Here are some answers that might help. I found the interval: (0,pi/2) The equation of the left vertical …