Co-ordinate geometry

 

If you are asked to:

 

Plot – this means draw accurately.

 

Sketch – approximately mark the point.

 

Draw – use an appropriate degree of accuracy that the question requires.

 

 

 

The gradient of a line is how slanted it is, the slope of a line. This is usually represented by the letter m.

 

To find the gradient of a line, it is the changes in y, divided by the changes in x. To do this, you’ll need the co-ordinates of two points on the line, but it is the difference between the y co-ordinate values divided by the difference between the x co-ordinate values. This is shown by:

 

M (Gradient) =	Y2-Y1
	X2-X1

 

It doesn’t matter which Y co-ordinate you call Y₁ or Y₂ or which X co-ordinate you call X₁ and X₂

 

Parallel lines have the same gradient, so if you have two parallel lines, the gradient of the line should be the same as the second one. The gradient of the first line (M₁) is equal to the gradient of the second line (M₂), M₁ = M_2.

 

Perpendicular lines are lines which cuts another line at 90 degrees. The gradients of perpendicular lines always multiply to make -1.

 

1

5

 

The reciprocal of a number is whatever that number must be multiplied by to make 1. So the reciprocal of 5 is :

 

 

 

3

2

 

They multiply to make 1. The reciprocal of a fraction is the upside down version of the fraction, so the reciprocal of

 

 

 

is :

 

2

3

 

 

 

 

 

 

 

If you know the co-ordinates of two points on a line, you can work out the distance between the two points, i.e. the length. If one of the points is called A and another called B, the distance of A to B (AB) is the √(x₂-x₁)² + (y₂-y₁)².

 

 

 

If you know two points on the line, you can workout the co-ordinates of the mid-point of the line with:

 

 

 

 

y-y1 = m(x-x₁)a