Coordinate Geometry

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What is the gradient (slope) of a line through points $(x_1, y_1)$ and $(x_2, y_2)$?

The gradient $m$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$.

What is the equation of a vertical line?

The equation of a vertical line through point $(a, b)$ is $x = a$.

What is the formula for finding the area of a triangle given its vertices?

Area = $\frac{1}{2} | x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) |$.

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