New
New
Year 11
Higher

Column vectors

I can represent information graphically given column vectors.

New
New
Year 11
Higher

Column vectors

I can represent information graphically given column vectors.

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Lesson details

Key learning points

  1. When translating, the entire shape moves.
  2. Although the point moves, the journey is not drawn.
  3. A vector can be drawn to show this journey.
  4. The vector is a straight line from the start to end point and covers the shortest distance.
  5. The top value is the distance left/right, the bottom value is the distance up/down.

Keywords

  • Vector - A vector can be used to describe a translation.

  • Displacement - Displacement is the distance from the starting point when measured in a straight line.

  • Vertex - A vertex is the point where two or more line segments meet. The plural is vertices.

Common misconception

When describing the movement of vectors, "across" is used to describe a horizontal movement.

Embed the understanding that "across" refers to the horizontal component, but the direction must be described concisely as a vector has direction and magnitude.

Pupils could draw their own pictures, words or patterns with straight line segments and write the column vectors to create it.
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).

Lesson video

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6 Questions

Q1.
A vector is used to describe which transformation?
Correct Answer: translation
Q2.
Match each vector to the displacement it describes.
Correct Answer:$$-2\choose-3$$,2 left, 3 down

2 left, 3 down

Correct Answer:$$2\choose-3$$,2 right, 3 down

2 right, 3 down

Correct Answer:$$2\choose3$$,2 right, 3 up

2 right, 3 up

Correct Answer:$$-2\choose3$$,2 left, 3 up

2 left, 3 up

Q3.
Which is the correct vector to translate the tail to the correct place on the elephant?
An image in a quiz
$$-2\choose3$$
$$2\choose3$$
$$2\choose-3$$
Correct answer: $$-2\choose-3$$
Q4.
Which is the correct vector to translate A to A'?
An image in a quiz
$$2\choose-4$$
Correct answer: $$2\choose4$$
$$4\choose2$$
$$-2\choose-4$$
Q5.
Which is the correct vector to translate A to A'?
An image in a quiz
$$-1\choose3$$
$$1\choose3$$
$$-3\choose-1$$
$$3\choose1$$
Correct answer: $$-1\choose-3$$
Q6.
Translate shape ABC by $$4\choose1$$.
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz

6 Questions

Q1.
A vector is a straight line from the start to end point and covers the distance.
Correct Answer: shortest, least
Q2.
A vector has (size) and direction.
Correct Answer: magnitude
Q3.
Which is the correct graphical representation of this vector? $$4\choose-3$$
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Q4.
The diagram shows the column vector $$a\choose-5$$. The value of $$a$$ is .
An image in a quiz
Correct Answer: 0
Q5.
The diagram shows the column vector $$a\choose-1$$ represents. The value of $$a$$ is .
An image in a quiz
Correct Answer: 6
Q6.
Match each vector to its best starting region.
An image in a quiz
Correct Answer:$$8\choose-5$$,Top left

Top left

Correct Answer:$$-8\choose-5$$,Top right

Top right

Correct Answer:$$-8\choose5$$,Bottom right

Bottom right

Correct Answer:$$8\choose5$$,Bottom left

Bottom left