Coordinate+Geometry+page

=Gradient=

Here is the formula for gradient. It can be rephrased as "rise over run". (x1, y1) and (x2, y2) are 2 points. The distance between the ys is the rise (yes, it rhymes!). The difference in the x values is the "run". Here is a diagram that illustrates this:



See this [|website] (animated explanation of gradient)

Equation of a line
Format is

y = m x + c
m is the gradient and c is the y intercept e.g. blue graph has y intercept of -2 and gradient of 4. Its equation is y = 4x - 2 e.g. red graph has y intercept of 1 and gradient of 2/3. Its equation is y =2/3 x + 1

=Equation from a point and a gradient - three methods=

Method 1: use the formula y - y1 = m (x - x1)
Need to know: y and x stay unchanged. (x1, y1) are numbers from a point. m is gradient. e.g. give the equation of a line that passes through (2, 5) with a gradient of 3

y - y1 = m (x - x1) substitute point and gradient values in y - 5 = 3 (x - 2) expand brackets y - 5 = 3x - 6 rearrange to finish equation (add 5 both sides) y = 3x - 1

Method 2: Substitute into the general rule and work out y intercept.
e.g. give the equation of a line that passes through (1, 4) with a gradient of -2 y = mx + c substitute values from point and gradient for x, y, m 4 = -2*1 + c calculate c. C is the y intercept 4 = -2 + c c = 6 Use m and c to write the completed equation.

Equation is y = -2x + 6

Method 3: Use the gradient to work backwards from the point and find the y intercept.
e.g. give the equation of a line that passes through (2, 7) with a gradient of 4.

Gradient of 4 means every point is 4 units higher than the previous one. So the points BEFORE the one given are 4 lower each time: (1, 3) and (0, -1) (0, -1) is the y intercept (y axis has x value of 0)

Rule is y = 4x - 1

=Distance and Midpoint= The distance between two points has this flash formula:  This can be restated as:

Distance2 = rise2 + run2

In other words, **Pythagoras’ Theorem.**

The midpoint between two points has this formula:  What you are actually doing is averaging the x values and averaging the y values.

In other words, if you want to simplify these formulae

For distance: use Pythagoras. The rise and run are the two short sides of the right-angled triangle.

Midpoint is (average x, average y).