Dividing a line in a given ratio (AQA GCSE Further Maths): Flashcards

Finds coordinates of point dividing line in given ratio

$\left(\frac{qx_1+px_2}{p+q}, \frac{qy_1+py_2}{p+q}\right)$

Point between two given points on line segment

Both horizontal and vertical

Weighted averages

$\frac{qx_1 + px_2}{p + q}$

$\frac{qy_1 + py_2}{p + q}$

Distance A to C vs C to B in ratio $p:q$

$AC:CB$ differs from $AC:AB$

First point's coordinate × second ratio number (e.g., $x_1$ × $q$)

Check geometric sense with ratio

Ratios act as weights for endpoint coordinates