Enlargement

Worked example

1. 1

   $\text{centre }(2,1),\text{scale factor }2,\text{corner }(3,2)$ — Start from the centre. Every corner is measured from it.

2. 2

   $3-2=1\text{ right},2-1=1\text{ up}$ — Take the centre's coordinates away from the corner's (or count squares) to see how far across and up it is.

3. 3

   $1\times 2=2\text{ right},1\times 2=2\text{ up}$ — Multiply both moves by the scale factor. The image corner is twice as far from the centre, in the same direction.

4. 4

   $(3,2)\to (2+2,1+2)=(4,3)$ — Add the new moves to the centre.

5. 5

   $(5,2):5-2=3\text{ right},2-1=1\text{ up}$ — Second corner: its moves from the centre.

6. 6

   $3\times 2=6\text{ right},1\times 2=2\text{ up}$ — Multiply both moves by 2.

7. 7

   $(5,2)\to (2+6,1+2)=(8,3)$ — Add the new moves to the centre.

8. 8

   $(3,3):3-2=1\text{ right},3-1=2\text{ up}$ — Third corner: its moves from the centre.

9. 9

   $1\times 2=2\text{ right},2\times 2=4\text{ up}$ — Multiply both moves by 2.

10. 10

    $(3,3)\to (2+2,1+4)=(4,5)$ — Add the new moves to the centre.

Worked example

1. 1

   $\text{centre }(1,1),\text{scale factor }\frac{1}{2},\text{corner }(9,1)$ — Start from the centre, as always.

2. 2

   $9-1=8\text{ right},1-1=0\text{ up}$ — Corner minus centre gives the moves from the centre.

3. 3

   $8\times \frac{1}{2}=4\text{ right},0\times \frac{1}{2}=0\text{ up}$ — A scale factor of one half makes the corner half as far from the centre.

4. 4

   $(9,1)\to (1+4,1+0)=(5,1)$ — Add the shorter moves to the centre. The image is closer to the centre.

5. 5

   $(5,5):5-1=4\text{ right},5-1=4\text{ up}$ — Second corner: its moves from the centre.

6. 6

   $4\times \frac{1}{2}=2\text{ right},4\times \frac{1}{2}=2\text{ up}$ — Halve both moves.

7. 7

   $(5,5)\to (1+2,1+2)=(3,3)$ — Add the halved moves to the centre.

8. 8

   $(5,1):4\text{ right},0\text{ up}\to 2\text{ right},0\text{ up}$ — Third corner: its moves from the centre are 4 and 0. Halving them gives 2 and 0.

9. 9

   $(5,1)\to (1+2,1+0)=(3,1)$ — Add the halved moves to the centre.

Worked example

1. 1

   $\text{centre }(0,0),k=3,\text{corner }(2,1)$ — From the origin, the corner's coordinates are its moves from the centre.

2. 2

   $(3\times 2,3\times 1)$ — Multiply each coordinate by the scale factor 3.

3. 3

   $(2,1)\to (6,3)$ — Work out each product.

4. 4

   $(4,1)\to (3\times 4,3\times 1)=(12,3)$ — Same rule for the next corner.

5. 5

   $(2,3)\to (3\times 2,3\times 3)=(6,9)$ — And for the last corner.

Worked example

1. 1

   $\text{centre }(0,0),k=\frac{1}{2},\text{corner }(-6,4)$ — A fraction scale factor makes the image smaller.

2. 2

   $\frac{1}{2}\times (-6)=-3$ — Half of −6 is −3. A positive scale factor does not change the sign.

3. 3

   $\frac{1}{2}\times 4=2$ — Half of 4 is 2.

4. 4

   $(-6,4)\to (-3,2)$ — Write the two new coordinates together.

Worked example

1. 1

   $4.8\text{ cm by }6.5\text{ cm},k=2.5$ — Every length is multiplied by the scale factor. Do each side on its own.

2. 2

   $4.8\times 2.5=12$ — Multiply the first side by 2.5.

3. 3

   $6.5\times 2.5=16.25$ — Multiply the second side by 2.5.

4. 4

   $12\text{ cm by }16.25\text{ cm}$ — Both sides got longer, as they should when the scale factor is bigger than 1.

Worked example

1. 1

   $\text{image }18\text{ cm},k=1.5$ — We want the object side, which is the one that was multiplied.

2. 2

   $\text{object}=\text{image}÷k$ — Dividing undoes multiplying.

3. 3

   $18÷1.5=12$ — Work it out. The object side is 12 cm.

4. 4

   $12\times 1.5=18$ — Check: multiply back and you get the image side.

Worked example

1. 1

   $\text{object }(2,2),(3,2),(2,3)\text{image }(3,3),(5,3),(3,5)$ — Matching corners are in the same order on both shapes.

2. 2

   $\text{object side }3-2=1,\text{image side }5-3=2$ — Measure the same side on both shapes: the bottom edge.

3. 3

   $\text{scale factor}=\frac{2}{1}=2$ — Scale factor is image side divided by object side.

4. 4

   $(2,2)\text{ and }(3,3)$ — Draw a long straight line through one pair of matching corners.

5. 5

   $(2,3)\text{ and }(3,5)$ — Draw a second line through another matching pair. One line is not enough, you need two.

6. 6

   $\text{lines cross at }(1,1)$ — The centre is the point where the lines cross. A third pair, (3, 2) and (5, 3), also passes through it.

7. 7

   $(1,1)\to (2,2):1\text{ right},1\text{ up}(1,1)\to (3,3):2\text{ right},2\text{ up}$ — Check: the image corner is twice as far from the centre as the object corner.