Translation

Worked example

1. 1

   $\left(\begin{array}{c}-4\\ 3\end{array}\right)$ — Top number: −4 means 4 left. Bottom number: 3 means 3 up. Every corner makes this same move.

2. 2

   $(2,-1):2+(-4)=-2$ — Add the top number to the corner's x-coordinate. Adding −4 moves 4 left.

3. 3

   $-1+3=2$ — Add the bottom number to the same corner's y-coordinate. Adding 3 moves 3 up.

4. 4

   $(2,-1)\to (-2,2)$ — Write the new x and y together as the image of this corner.

5. 5

   $(4,-1)\to (4+(-4),-1+3)$ — Second corner, same move: add −4 to x and 3 to y.

6. 6

   $=(0,2)$ — Work out each bracket: 4 − 4 = 0 and −1 + 3 = 2.

7. 7

   $(2,1)\to (2+(-4),1+3)$ — Third corner, same move: add −4 to x and 3 to y.

8. 8

   $=(-2,4)$ — Work out each bracket: 2 − 4 = −2 and 1 + 3 = 4.

9. 9

   $(-2,2),(0,2),(-2,4)$ — Join the three image points. The image is the same size and faces the same way as the object.

Worked example

1. 1

   $(-1,3)\to (4,1)$ — Pick one corner of the object and the same corner on the image.

2. 2

   $4-(-1)=4+1=5$ — Across is image x minus object x. Taking away −1 adds 1, so the move is 5 to the right.

3. 3

   $1-3=-2$ — Up or down is image y minus object y. A negative answer means down, so 2 down.

4. 4

   $\left(\begin{array}{c}5\\ -2\end{array}\right)$ — Write the across number on top and the up or down number underneath.

5. 5

   $(-1+5,3+(-2))=(4,1)$ — Check: add the vector to the object corner. It lands on the image corner.

Worked example

1. 1

   $(d,2)\text{by}\left(\begin{array}{c}3\\ e\end{array}\right)\text{to}(7,-4)$ — The object point has a letter for x. The vector has a letter on the bottom. The image point is known.

2. 2

   $d+3=7$ — Across row: object x plus the top number equals image x.

3. 3

   $d=7-3=4$ — Take 3 from both sides to get d on its own.

4. 4

   $2+e=-4$ — Up or down row: object y plus the bottom number equals image y.

5. 5

   $e=-4-2=-6$ — Take 2 from both sides. −4 − 2 = −6, so the move is 6 down.

6. 6

   $(4+3,2+(-6))=(7,-4)$ — Check: move (4, 2) by the vector (3, −6). It lands on the image point.