Parallel and perpendicular lines on coordinate axes | Maths

Starter quiz

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

'circle' ✓
A(n) ______ of a circle is part of the circle’s circumference.

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

a ✓

b

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

$y = 5-{1\over 3}x$

$y = {1\over 3}x + 5$

$y = 5 - 3x$

$y = 3x + 5$ ✓
The gradient of the line which passes through the points (4, 8) and (7, 14) is ______.

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

$y = -{3\over 2}x + 1$ ✓

$y = -{2\over 3}x + 1$

$y = {2\over 3}x + 1$

$y = 1 - 4x$

$y = 4x + 1$

Exit quiz

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

A line which intersects AB at point A.

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

a

b ✓

c ✓

d
Match each diagram to the correct description.

Diagram a

⇔

a perpendicular bisector of PQ ✓

Diagram b

⇔

a bisector of PQ ✓

Diagram c

⇔

a perpendicular to PQ ✓

Diagram d

⇔

a line parallel to PQ ✓
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?

$y = -{1\over 3}x + 2$

$y = {1\over 3}x - 2$

$y = {1\over 3}x + 2$ ✓

$y = x$

$y = x-2$
Izzy plots the points A, B, C and D. Given ABDC is a rhombus, which of these statements have to be true?

Adjacent sides are perpendicular.

Opposite sides are parallel. ✓

The diagonals are the same length.

The diagonals are perpendicular to each other. ✓
Why is shape ABDC not a parallelogram?

AB and CD are not parallel

AC and BD are not parallel ✓

AC and CD are not perpendicular

AB and AC are different lengths

Worksheet

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Lesson Details

Key learning points

Parallel lines have the same gradient.
The product of the gradients of two perpendicular lines is -1
Your knowledge of the geometrical properties of shapes can be applied here.

Common misconception

Pupils may not appreciate all the steps required to prove what type of shape is shown.

A warm-up for the lesson could be to review properties of shapes. Consider describing a shape, one property at a time. How much information is needed before pupils can be certain they know which shape is being described?

Keywords

Perpendicular - Two lines are perpendicular if they meet at right angles.
Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.