How to translate a shape on a coordinate grid using a vector. Math help.

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How To Translate A Shape Video

If you are asked to translate a shape then you need to move the shape to a new position on the coordinate grid. Usually, the directions of the translation are given in terms of a vector. The vector contains 2 numbers which are written vertically (instead of horizontally like a coordinate).

The top number of the vector tells you if you are moving the shape left or right. If the number is negative you move the shape left. If the number is positive you move the shape right.

The bottom number of the vector tells you if you are moving the down or up. If the number is negative you move the shape down. If the number is positive you move the shape up.

Example 1

Translate the triangle on the coordinate grid by the vector:

Since the question is asking you to translate the shape you need to move the shape to a new position onto the coordinate grid. Since the top number of the vector is -5, this means that you need to move the shape 5 square left. The bottom number of the vector is 1, so you also need to move the shape 1 square up. Therefore, move each vertex (corner) of the triangle 5 squares left and 1 square up. Make sure you count all 3 corners of the triangle so you don’t make any mistakes.

Example 2

The coordinate grid shows 2 identical flags. What vector translates the red flag onto the blue flag?

All you need to do is pick 2 corresponding points on both flags. Picking the points at the bottom of both flags seems the most sensible. Now to move the bottom of the red flag to the bottom of the blue flag you need to move the point 6 squares right and 4 square down.

Therefore, put 6 on the top of the vector (positive 6 as the shape is moving right)

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And put -4 on the bottom of the vector (negative 4 as the shape is moving down).

So the vector that you need is:

Question: How to find coordinates A (0,-2) under translation (-1/2)?

Answer: The coordinate needs to be moved 1 left and 2 up.

So subtract 1 off the x coordinate to give -1, and add 2 the y coordinate to give 0.

This will give a final answer of (-1, 0).

Question: Move point A (-12,10) using the vector <-8,-1>?

Answer: The vector means movr point A 8 squares left and 1 square down.

To do this subtract 8 from the x coordinate (-12) to give -20, and subtract 1 from the y coordinate to give (10) to give 9.

So the final point will be at (-20,9).

Question: How can you tell when you need to move a shape left or right on a coordinate grid?

Answer: If the top number is negative move the shape left. If the top number is positive move the shape right.

Question: Move point A(0,3) using vector ( -1,-1)?

Answer: The vector means move the point A 1 square left and 1 square down.

So the new point will be at (-1, 2)

mkpop on December 26, 2016:

thnxx a lot its a great explanation .... ^_^

Gareth on May 07, 2013:

This helped me a lot, Thanks!

k on May 26, 2012:

fantastic

MazioCreate from Brisbane Queensland Australia on September 01, 2011:

catman3000 you've done it again! Simple explanations that make understanding these concepts soooooo easy.

rockdresses from Turkey on September 01, 2011:

very useful~

Kimberly Schimmel from North Carolina, USA on September 01, 2011:

Very good explanation.