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Year 10
Higher

Parallel and perpendicular lines on coordinate axes

I can solve problems involving parallel/perpendicular lines on coordinate axes.

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Share activities with pupils
New
New
Year 10
Higher

Parallel and perpendicular lines on coordinate axes

I can solve problems involving parallel/perpendicular lines on coordinate axes.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Parallel lines have the same gradient.
  2. The product of the gradients of two perpendicular lines is -1
  3. 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.

Pupils may need a more in-depth review of constructions before this lesson. If so, the unit on constructions could be used (Year 8 Unit 10).
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
A(n) is a shape such that every point on the circumference is equidistant to its centre.
Correct Answer: circle
Q2.
A(n) of a circle is part of the circle’s circumference.
Correct Answer: arc
Q3.
Which of these compass widths are suitable when constructing the perpendicular bisector of the given line segment?
An image in a quiz
Correct answer: a
b
Correct answer: c
Q4.
Which of these is an equation of a line perpendicular to the line with equation $$y = 1-{1\over 3}x$$?
$$y = 5-{1\over 3}x$$
$$y = {1\over 3}x + 5$$
$$y = 5 - 3x$$
Correct answer: $$y = 3x + 5$$
Q5.
The gradient of the line which passes through the points (4, 8) and (7, 14) is .
Correct Answer: 2
Q6.
Which of these are equations of a line parallel to the line which passes through coordinates (5, -2) and (-3, 10)?
Correct answer: $$y = -{3\over 2}x + 1$$
$$y = -{2\over 3}x + 1$$
$$y = {2\over 3}x + 1$$
$$y = 1 - 4x$$
$$y = 4x + 1$$

Exit quiz

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6 Questions

Q1.
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.
Correct answer: A line which intersects AB at a right angle and cuts the line segment in half.
Q2.
Which of these constructions can be used to draw on the perpendicular bisector of the line segment given?
An image in a quiz
a
Correct answer: b
Correct answer: c
d
Q3.
Match each diagram to the correct description.
An image in a quiz
Correct Answer:Diagram a,a perpendicular bisector of PQ

a perpendicular bisector of PQ

Correct Answer:Diagram b,a bisector of PQ

a bisector of PQ

Correct Answer:Diagram c,a perpendicular to PQ

a perpendicular to PQ

Correct Answer:Diagram d,a line parallel to PQ

a line parallel to PQ

Q4.
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?
An image in a quiz
$$ y = -{1\over 3}x + 2$$
$$ y = {1\over 3}x - 2$$
Correct answer: $$ y = {1\over 3}x + 2$$
$$ y = x$$
$$ y = x-2$$
Q5.
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.
Correct answer: Opposite sides are parallel.
The diagonals are the same length.
Correct answer: The diagonals are perpendicular to each other.
Q6.
Why is shape ABDC not a parallelogram?
An image in a quiz
AB and CD are not parallel
Correct answer: AC and BD are not parallel
AC and CD are not perpendicular
AB and AC are different lengths