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AQA GCSE · Question 03 · Geometry and Measures
The vector (<sup>-3</sup><sub>7</sub>) translates A to B. Write down the vector that translates B to A.
The vector (<sup>-3</sup><sub>7</sub>) translates A to B. Write down the vector that translates B to A.
How to approach this question
The translation from B to A is the exact opposite of the translation from A to B. To find the opposite vector, you multiply each component of the original vector by -1.
Full Answer
The vector that translates B to A is the reverse of the vector from A to B. To reverse a vector, you change the sign of each component.
So, the vector is (<sup>3</sup><sub>-7</sub>).
A vector describes a translation, which is a movement with a specific direction and magnitude. The vector (<sup>-3</sup><sub>7</sub>) means a movement of -3 units in the x-direction (3 units left) and +7 units in the y-direction (7 units up). To translate from B back to A, you must reverse this movement. The reverse movement is +3 units in the x-direction (3 units right) and -7 units in the y-direction (7 units down). Therefore, the vector that translates B to A is (<sup>3</sup><sub>-7</sub>).
Common mistakes
✗ Only changing the sign of one of the components, e.g., (<sup>-3</sup><sub>-7</sub>) or (<sup>3</sup><sub>7</sub>).
✗ Swapping the components, e.g., (<sup>7</sup><sub>-3</sub>).
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