Coordinate Geometry
Term 2
Distance · Midpoint · Gradient · Equation of a line
Learning Objectives
PrintPoints 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.
Gradient and Equation of a Line
- 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.
Parallel, Perpendicular and Applications
- 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.
Assessments
Coordinate geometry end-of-unit test
Criterion A
50 min
Written test on distance and midpoint formulas, gradient between two points, and finding the equation of a line given various pieces of information.
Review Pack
Open review hub
Fluency Pack A — 40 questions
Fluency Pack B — 40 questions
Problem-solving — 12 unfamiliar tasks
Worked solutions (Pack A + B + problems)