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Home/Tag: Coordinate Geometry
16 06, 2017

Point Gradient Formula y – y1 = m(x – x1) worked examples Find the equation of the line passing through  (2, -4) and (-3, 6).  $m=\frac{6-(-4)}{-3-2}$ $=\frac{10}{-5}$ m = -2  x1 = 2, y1 = -4 x2 = -3, y2 = 6 find gradient first using gradient formula [...]

16 06, 2017

## Two Point Formula

By |2017-06-16T12:10:57+10:00June 16th, 2017||Comments Off on Two Point Formula

Two Point Formula $\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$  worked examples Find the equation of the line passing through (2, -4) and (-3, 6).   $\frac{y-(-4)}{x-2}=\frac{6-(-4)}{-3-2}$  x1 = 2, y1 = -4, x2 = -3, y2 = 6 substitute into the formula $\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ $\frac{y+4}{x-2}=\frac{10}{-5}$ $\frac{y+4}{x-2}=-2$ simplify y + 4 = -2(x -2) multiply both sides by (x - [...]

8 08, 2016

## Collinear Points

By |2016-10-21T13:16:59+10:00August 8th, 2016||Comments Off on Collinear Points

Collinear Points Points that lie on the same line to show points are collinear, show points have same gradient and common point worked examples Show the points (2, 4), (4, 6) and (6, 8) are collinear. $m_1=\frac{6-4}{4-2}$ find the gradient of the first two points using $m=\frac{y_2-y_1}{x_2-x_1}$ $m_1=\frac{2}{2}$ $m_1=1$ simplify [...]

8 08, 2016

## Midpoint

By |2016-10-21T13:16:59+10:00August 8th, 2016||Comments Off on Midpoint

Midpoint $MP=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ worked examples Find the midpoint the points (4, 3) and (2, 9). $MP=(\frac{4+2}{2},\frac{3+9}{2})$ using the formula $MP=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$, where x1 = 4 and y1 = 3 and x2 = 2 and y2 = 9, substitute $MP=(\frac{6}{2},\frac{12}{2})$ simplify (3, 6) calculate further examples [...]

8 08, 2016

Gradient $m=\frac{y_2-y_1}{x_2-x_1}$ $m=\frac{rise}{run}$ worked examples Find the gradient of the two points (4, 3) and (2, 9). $m=\frac{9-3}{2-4}$ using the formula $m=\frac{y_2-y_1}{x_2-x_1}$, where x1 = 4 and y1 = 3 and x2 = 2 and y2 = 9, substitute $d=\frac{6}{-2}$ simplify m = -3 calculate further examples [...]

8 08, 2016

## Distance

By |2016-10-21T13:16:59+10:00August 8th, 2016||Comments Off on Distance

Distance $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_1)^{2}}$ worked examples Find the distance between the points (4, 3) and (2, 9), correct to two decimal places. $d=\sqrt{(2-4)^{2}+(9-3)^{2}}$ using the formula $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_1)^{2}}$, where x1 = 4 and y1 = 3 and x2 = 2 and y2 = 9, substitute $d=\sqrt{4+36}$ simplify $d=\sqrt{40}$ calculate d = 6.32 [...]

6 06, 2016

Shading Regions   worked examples Shade the region y ≥ x + 1 on the number plane. x-intercept: y = 0 0 = x + 1 x = -1 First we sketch the line y = x + 1, it will be solid as it is ≥ (dotted if it was just [...]

22 08, 2015