Coordinate Geometry — Objectives | Mathematics Department

Points and Line Segments

1. Plot points on the Cartesian plane and identify the quadrant they lie in.
2. Calculate the distance between two points using $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
3. Calculate the midpoint of a line segment using $M = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)$.
4. Find the point that divides a line segment in a given ratio.

5. Understand gradient as a ratio (rise over run) and as $\tan\theta$ where $\theta$ is the angle with the $x$-axis.
6. Calculate the gradient between two points using $m = \dfrac{y_2 - y_1}{x_2 - x_1}$.
7. Write the equation of a line in the form $y = mx + c$ and identify the gradient and $y$-intercept.
8. Find the equation of a line given a point and the gradient, or given two points.
9. Sketch lines from their equation, including reading off $x$- and $y$-intercepts.

10. Identify parallel lines from equal gradients.
11. Identify perpendicular lines using $m_1 \cdot m_2 = -1$.
12. Find the equation of a line parallel or perpendicular to a given line through a given point.
13. Solve geometric problems on the Cartesian plane (e.g. show points form a right-angled triangle, parallelogram or rhombus).
14. Interpret gradient and intercept as rates of change in real-world linear contexts.