Coordinate Geometry: Straight Lines
Coordinate geometry of straight lines uses algebra to describe lines on the Cartesian plane, covering gradients, equations of lines, midpoints, distances, and the relationships between parallel and perpendicular lines. At Level 2 Further Maths it extends GCSE coordinate geometry to perpendicular bisectors, collinearity and geometric proof problems worth up to 9 marks.
Before you start
Make sure you're comfortable with these topics first:
Method
- Use gradient = (y2 - y1)/(x2 - x1) between two points to find the steepness of a line.
- Substitute a known point and gradient into y - y1 = m(x - x1), then rearrange into y = mx + c or ax + by + c = 0 as required.
- Remember parallel lines share the same gradient, and perpendicular lines have gradients that multiply to give -1.
- Use the midpoint formula ((x1+x2)/2, (y1+y2)/2) and the distance formula sqrt((x2-x1)^2+(y2-y1)^2) for lengths and midpoints, simplifying surd answers where asked.
- To find where two lines meet, set the two y-expressions equal to each other and solve the resulting equation.
- For collinearity, show the gradient between each pair of points is the same, referencing a shared point.
Worked example
Find the equation of the straight line that passes through the points A(2, -1) and B(6, 7), giving your answer in the form y = mx + c.
- Find the gradient: m = (7 - (-1))/(6 - 2) = 8/4 = 2.
- Substitute point A and the gradient into y - y1 = m(x - x1): y - (-1) = 2(x - 2).
- Expand: y + 1 = 2x - 4.
- Rearrange to make y the subject: y = 2x - 5.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Further Maths exam paper, with a full mark scheme.
Line l passes through the point (4, -2) and is parallel to the line with equation y = 5x + 3. Find the equation of l, giving your answer in the form y = mx + c.
Points A(1, 8) and B(5, 2) are two points. Find the equation of the perpendicular bisector of AB, giving your answer in the form y = mx + c.
Show that the points A(-2, -3), B(2, 1) and C(5, 4) are collinear.
Free printable worksheet
Want more practice on paper? Download the coordinate geometry: straight lines worksheet pack - 13 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.