Modelling with Straight Lines (Edexcel A-Level Mathematics): Flashcards

$m = (y_2 - y_1) / (x_2 - x_1)$ for points $(x_1, y_1)$ and $(x_2, y_2)$.

Midpoint = $((x_1 + x_2)/2, (y_1 + y_2)/2)$ for endpoints.

Length = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ between endpoints.

It represents the line with gradient $-2$ through $(3, 5)$.

Use distance formula and Pythagoras' Theorem for $AB$.

The distance $AB$ is $6\sqrt{5}$ between points $A$ and $B$.

Expand and simplify to find $x$ values of the equation.

$x = 9$ or $x = -3$ from $(x - 9)(x + 3) = 0$.

$y = -7$ for $x = 9$; $y = 17$ for $x = -3$.

Point $B$'s new coordinates are $(9, -7)$ after the transform.