New
New
Year 8

Perpendicular to a given line through a given point

I can use the properties of a rhombus to construct a perpendicular to a given line through a given point.

New
New
Year 8

Perpendicular to a given line through a given point

I can use the properties of a rhombus to construct a perpendicular to a given line through a given point.

Lesson details

Key learning points

  1. A rhombus can be constructed from two congruent isosceles triangles.
  2. This can be used to construct a perpendicular to a line through a point.
  3. This perpendicular has special properties that can be investigated.
  4. Shortest distances can be found using constructions with perpendicular lines.

Common misconception

You can't accurately draw the perpendicular to a point on a line segment close to its endpoint.

The perpendicular to a line segment through any point can be found; some line segments just require extending in length first.

Keywords

  • Bisect - To bisect means to cut or divide an object into two equal parts.

  • Rhombus - A rhombus is a parallelogram where all sides are the same length.

Whilst circles of any radius can be used to modify the length of a line segment, the bigger the circle, the smaller the influence of any imprecision in the construction process.
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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6 Questions

Q1.
This quadrilateral is a kite. Find the value of angle $$a$$, in degrees.
An image in a quiz
Correct Answer: 100, 100 degrees, 100degrees, 100°
Q2.
This diagram shows an accurate construction of a perpendicular bisector. YZ has a length of 8.4 cm. Which of these is the smallest value of $$r$$ that can be used in this construction?
An image in a quiz
2.1 cm
Correct answer: 4.3 cm
8.4 cm
16.8 cm
8.4$$\pi$$ cm
Q3.
Match the sentence to the diagram.
An image in a quiz
Correct Answer:a,A bisector to line segment QV

A bisector to line segment QV

Correct Answer:b,A perpendicular to line segment QV

A perpendicular to line segment QV

Correct Answer:c,A perpendicular bisector to line segment QV

A perpendicular bisector to line segment QV

Correct Answer:d,An intersecting line to line segment QV

An intersecting line to line segment QV

Q4.
This is an incomplete construction to find the perpendicular bisector of YZ. Which of these steps is missing from this construction?
An image in a quiz
A circle with centre at point Y.
A line segment connecting the intersection to point Z.
Correct answer: An arc below YZ with centre at point Z.
An arc above YZ with centre at point Z.
Correct answer: A line through two pairs of intersecting arcs.
Q5.
This is an accurate construction to draw a rhombus. What is the perimeter (in cm) of the rhombus that can be drawn from this construction?
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Correct Answer: 56, 56 cm, 56cm
Q6.
Sofia starts her construction of a perpendicular bisector to EF. She is about to move the pair of compoasses to construct a second circle. Which of these statements are true?
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Sofia needs to place the compass needle at the midpoint of EF.
Sofia should draw a circle with centre at the intersection of EF and the circle.
Sofia needs to draw an arc with centre at point F next.
Correct answer: Sofia should adjust the compass width so that both circles drawn are congruent.
Correct answer: Currently, the next circle Sofia draws will be smaller than the first.

6 Questions

Q1.
The line segment EF has been shortened by constructing a circle of radius 8 cm, with a centre at point K. What is the length (in cm) of the shortened line segment?
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Correct Answer: 16, 16 cm, 16cm
Q2.
Which of these diagrams shows the most appropriate first step when constructing the perpendicular to line segment TU through point Z?
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a
b
c
Correct answer: d
Q3.
Izzy has shortened line segment LM by drawing a circle with centre at point Z. Izzy wants to draw four arcs of radius $$k$$ cm to construct a perpendicular. What value must $$k$$ be greater than?
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4 cm
6 cm
Correct answer: 12 cm
14 cm
28 cm
Q4.
A line segment is extended so that a perpendicular can be constructed through point Z. Which of these diagrams shows a suitable extension of the line segment?
An image in a quiz
a
Correct answer: b
c
d
Q5.
Which of these four circles can help in the construction of the perpendicular to line segment WU through point Z?
An image in a quiz
a
Correct answer: b
Correct answer: c
d
Q6.
Match the values to their statements.
An image in a quiz
Correct Answer:14 cm,the shortest distance from X to an extension of JK

the shortest distance from X to an extension of JK

Correct Answer:15 cm,the shortest distance from X to line segment JK

the shortest distance from X to line segment JK

Correct Answer:17 cm,the radius of circle with centre at point X

the radius of circle with centre at point X

Correct Answer:28 cm,the shortest distance from X to point J

the shortest distance from X to point J