Dilations & Similarity — Drills
Dilations & Similarity has 6 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 14 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Scale factor — The number every length is multiplied by.
- Similar figures — Same shape, different size: equal angles, proportional sides.
- Corresponding sides — Sides in matching positions in two similar figures.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Volume — Space inside, in cubic units.
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Factor — A number that divides evenly into another.
- Scale — What one grid step is worth — and where the axis starts.
- Dilation — A resizing from a centre point by a scale factor k.
- Similar — Same shape, possibly different size. Written △ ABC ∼ △ DEF.
- Corresponding angles — Same position at each crossing. Equal when the lines are parallel.
- Segment — Two endpoints and everything between them. Written AB.
- Height — The perpendicular distance from the base to the opposite corner.
Dilate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Dilate (-4, -4) by a scale factor of 3, centred at the origin.
Worked answer
(-12, -12)
-4 × 3 = -12
-4 × 3 = -12
The image is (-12, -12).
Problem 2
Dilate (3, 2) by a scale factor of 4, centred at the origin.
Worked answer
(12, 8)
3 × 4 = 12
2 × 4 = 8
The image is (12, 8).
Factoring
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A side of length 4 becomes 20 after a dilation. Find the scale factor.
Worked answer
5
k = 204
k = 5
Greater than one, so it enlarged.
Problem 2
A side of length 6 becomes 24 after a dilation. Find the scale factor.
Worked answer
4
k = 246
k = 4
Greater than one, so it enlarged.
Similar
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
△ ABC ∼ △ DEF with AB = 8, DE = 32 and BC = 4. Find EF.
Worked answer
16
k = 328 = 4
EF = 4 × 4
EF = 16
Problem 2
△ ABC ∼ △ DEF with AB = 2, DE = 8 and BC = 9. Find EF.
Worked answer
36
k = 82 = 4
EF = 4 × 9
EF = 36
Perimeter
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A polygon has perimeter 10. It is dilated by a factor of 4. Find the new perimeter.
Worked answer
40
Every side is multiplied by 4.
So the perimeter is too.
10 × 4 = 40
Problem 2
A polygon has perimeter 16. It is dilated by a factor of 3. Find the new perimeter.
Worked answer
48
Every side is multiplied by 3.
So the perimeter is too.
16 × 3 = 48
Area
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A figure has area 28 cm2. After a dilation with k = 4, find the new area.
Worked answer
448
k2 = 16
28 × 16 = 448
448 cm2
Problem 2
A figure has area 6 cm2. After a dilation with k = 4, find the new area.
Worked answer
96
k2 = 16
6 × 16 = 96
96 cm2
Volume
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A solid is dilated by a factor of 2. By what factor does its volume grow?
Worked answer
8
k3 = 23
= 8
Length × 2, area × 4, volume × 8.
Problem 2
A solid is dilated by a factor of 3. By what factor does its volume grow?
Worked answer
27
k3 = 33
= 27
Length × 3, area × 9, volume × 27.