Negative Enlargement

Worked example

1. 1

   $(2,2)-(1,1)=(1,1)$ — Start at the centre and go to the first corner. Take the centre away from the corner: 2 − 1 = 1 across and 2 − 1 = 1 up.

2. 2

   $(1,1)\times (-2)=(-2,-2)$ — Multiply both numbers by the scale factor −2. The 2 makes the move twice as long and the minus sign turns each direction round: 2 left and 2 down.

3. 3

   $(1,1)+(-2,-2)=(-1,-1)$ — Start from the centre again and add the new move: 1 + (−2) = −1 and 1 + (−2) = −1. This is the first image corner.

4. 4

   $(4,2)-(1,1)=(3,1)$ — Do the same for the next corner. From the centre it is 3 across and 1 up.

5. 5

   $(3,1)\times (-2)=(-6,-2)$ — Multiply by −2: 3 × (−2) = −6 and 1 × (−2) = −2. That is 6 left and 2 down.

6. 6

   $(1,1)+(-6,-2)=(-5,-1)$ — Add the move to the centre: 1 + (−6) = −5 and 1 + (−2) = −1. This is the second image corner.

7. 7

   $(2,3)-(1,1)=(1,2)$ — Now the last corner. From the centre it is 1 across and 2 up.

8. 8

   $(1,2)\times (-2)=(-2,-4)$ — Multiply by −2: 1 × (−2) = −2 and 2 × (−2) = −4. That is 2 left and 4 down.

9. 9

   $(1,1)+(-2,-4)=(-1,-3)$ — Add the move to the centre: 1 + (−2) = −1 and 1 + (−4) = −3. Join the three image corners to finish.

Worked example

1. 1

   $AB=1,A^{\prime }{B}^{\prime }=2$ — Pick a pair of matching sides and measure them. A(3, 2) to B(4, 2) is 1 long. A′(0, −1) to B′(−2, −1) is 2 long.

2. 2

   $\frac{2}{1}=2$ — Image side ÷ object side gives the size of the scale factor, with no sign yet.

3. 3

   $\text{scale factor }-2$ — AB points right but A′B′ points left, so the image is upside down. That makes the factor negative.

4. 4

   $(3,2)\to (2,1)\to (1,0)\to (0,-1)$ — Join A to A′ with a straight line. Each step is 1 left and 1 down, and the line goes through (2, 1).

5. 5

   $(4,2)\to (2,1)\to (0,0)\to (-2,-1)$ — Join B to B′. Each step is 2 left and 1 down, and this line also goes through (2, 1).

6. 6

   $\text{centre }(2,1)$ — The two lines cross at (2, 1), between the shapes. That is the centre.

7. 7

   $(3,2)-(2,1)=(1,1),(0,-1)-(2,1)=(-2,-2)$ — Check with corner A. Its move from the centre is (1, 1) and its image’s move is (−2, −2), which is −2 times as much.

8. 8

   $\text{Enlargement, scale factor }-2,\text{centre }(2,1)$ — Give the name, the scale factor with its minus sign, and the centre. Each one is a mark.

Worked example

1. 1

   $(7,6)-(3,2)=(4,4)$ — Go from the centre (3, 2) to the corner: 7 − 3 = 4 across and 6 − 2 = 4 up.

2. 2

   $(4,4)\times \left(-\frac{1}{2}\right)=(-2,-2)$ — Multiply both numbers by −½. Half of 4 is 2, so the move is half as long, and the minus sign reverses it: 2 left and 2 down.

3. 3

   $(3,2)+(-2,-2)=(1,0)$ — Add the move to the centre: 3 + (−2) = 1 and 2 + (−2) = 0. This is the image corner.