Coordinate Geometry

Core 1

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  • Created by: Rayssa
  • Created on: 22-04-10 20:50

Midpoints

Midpoint of AB= (x1+x2/2, y1+y2/2)

The distance AB= (root)(x2-x1)sqr+(y2-y1)sqr (pythagoras)

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Questions

A=(7, -10) B=(4, -8)

Find the midpoint

Find the length of line AB.

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Gradients

The gradient of AB is y1-y2/x1-x2

If two lines have the same gradient, they are parallel

two lines are perpendicular if the angle between them is 90deg.

the product of these lines are -1

m2-m1=-1

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Questions

A= (6,7) B=(5,-4)

Find the gradient.

Find the gradient of the line perpendicular to this line.

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y=mx+c

The equation of a straight line is y=mx+c

m is the gradient and c is the y-intercept

Another equation of a straight line is y-y1=m(x-x1)

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Questions

Find the equation of the line through the points A and B

A is at (3,2) and B is at (6,11)

A is at (-1,2) and B is at (1,12)

A is at (-5,-3) and B is at (4,1)

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Intersecting lines

use simultaneous equations to find the point where these two lines intersect:

if there are two y= or x=, put both equations equal each other.

If there is just one question with 1 y or x=, replace the y or x in the other equation with the equation y or x=.

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Question

The edges of triangle ABC are given by the equations:

x-y=8

5x-2y=10

y=28-3x

Find the coordinates of vertices A, B and C.

Start with a sketch

choose a pair of equations and solve simultaneously

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