Two lines are perpendicular if they meet at right angles.

Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

Parallel and perpendicular lines on coordinate axes

Maths

The work on gradient in this unit is expanded further in the future unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

A line which is parallel to AB and the same length. 

A line which passes through the middle of the segment AB.

A line which is the same length as AB but is a 90 degree rotation. 

A line which intersects AB at a right angle and cuts the line segment in half. 

Which of these statements best describes a perpendicular bisector of a line segment AB?

Which of these constructions can be used to draw on the perpendicular bisector of the line segment given?

Match each diagram to the correct description.

Point A has coordinates (4, 10) and Point B has coordinates (8, -2). The midpoint of AB has coordinates (6, 4). What is the equation of the perpendicular bisector of AB?

The diagonals are perpendicular to each other.

Izzy plots the points A, B, C and D. Given ABDC is a rhombus, which of these statements have to be true?

A(n) {{ }} is a shape such that every point on the circumference is equidistant to its centre.

A(n) {{ }} of a circle is part of the circle’s circumference.

Which of these compass widths are suitable when constructing the perpendicular bisector of the given line segment?

Which of these is an equation of a line perpendicular to the line with equation $$y = 1-{1\over 3}x$$?

The gradient of the line which passes through the points (4, 8) and (7, 14) is {{ }}.

Which of these are equations of a line parallel to the line which passes through coordinates (5, -2) and (-3, 10)?

This lesson will be removed by end of Summer Term 2025.

Parallel and perpendicular lines on coordinate axes

Lesson outcome

This lesson will be removed by end of Summer Term 2025.