Dilation — Grade 8 Math, what it means and where it is taught
A resizing from a centre point by a scale factor k.
Taught in Grade 8 Math.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Scale factor — The number every length is multiplied by.
Practise this idea
6 questions in the course bank use Dilation, in Congruence & Sequences of Transformations, Dilations & Similarity.
Problem 1
Which sequence guarantees the image is congruent to the original?
- Reflect, then translate
- Dilate by 2, then translate
- Reflect, then dilate by 3
- Dilate by 12, then rotate
Worked answer
Reflect, then translate
Reflections and translations are both rigid
Dilations are not, unless k = 1
So the first sequence is the only one
Problem 2
A side of length 5 becomes a side of length 15 after a dilation. Find the scale factor.
Worked answer
3
k = 155
k = 3
Problem 3
A dilation has k = 0.4. The image is
- smaller than the original
- larger than the original
- the same size
- turned upside down
Worked answer
smaller than the original
0.4 < 1
So every distance shrinks
The image is smaller
Problem 4
A triangle has area 12 cm2. After a dilation with k = 2, find the new area.
Worked answer
48
k2 = 4
12 × 4 = 48
48 cm2
Problem 5
Which is always true for two similar figures?
- Corresponding angles are equal
- Corresponding sides are equal
- Perimeters are equal
- Areas are equal
Worked answer
Corresponding angles are equal
Angles never change under a dilation
Sides change by the factor k
So only the angle statement is always true
Problem 6
A dilation centred at (0, 0) maps (6, -9) to (-4, 6). Find k.
Worked answer
-2/3
-46 = -23
Check the other: 6-9 = -23 ✓
k = -23 — a negative factor also turns the figure 180°