Try each question on paper first. The questions follow the skills in congruency, enlargement and combined transformations.
Use the transformation coordinates explorer afterwards to test your coordinate answers.
Questions
Q1. Triangle ABC has sides 6 cm, 7 cm and 9 cm. Triangle PQR has sides 9 cm, 6 cm and 7 cm.
Are they congruent? Give the reason.
Answer
All three pairs of sides are equal: 6 and 6, 7 and 7, 9 and 9. The triangles are congruent by SSS.
Q2. Two triangles each have angles of 40°, 60° and 80°, but no sides are given. Can you say they are congruent?
Answer
No. Equal angles only show the triangles have the same shape, so they are similar. A side length is needed to fix the size, for example by ASA or AAS.
Q3. A line of 5 cm is enlarged to 12 cm. Find the scale factor.
Answer
k = 12 ÷ 5 = 2.4.
Q4. A shape of area 15 cm² is enlarged with scale factor 4. Find the image area.
Answer
Image area = 4² × 15 = 16 × 15 = 240 cm².
Q5. The object area is 32 cm² and the image area is 98 cm². Find the scale factor.
Answer
k² = 98 ÷ 32 = 3.0625, so k = √3.0625 = 1.75.
Check: 1.75² × 32 = 3.0625 × 32 = 98.
Q6. An enlargement maps P(3, 2) to P’(5, 4) and Q(3, 1) to Q’(5, 2). Find the centre of the enlargement.
Answer
Line PP’ passes through (3, 2) and (5, 4), so y = x − 1.
Line QQ’ passes through (3, 1) and (5, 2), with gradient 1/2, so y − 1 = (x − 3)/2.
Set x − 1 = 1 + (x − 3)/2, so 2x − 2 = 2 + x − 3. Then x = 1 and y = 0. The centre is (1, 0), and k = 2.
Q7. T is the translation by (−2, 4), and R is the reflection in the x-axis. Find RT(3, 1) and TR(3, 1).
Answer
RT: T first gives (1, 5), then R gives (1, −5).
TR: R first gives (3, −1), then T gives (1, 3).
The order changes the image.
Q8. A segment of 9 cm is reduced to 6 cm. An object area of 27 cm² is reduced by the same transformation. Find the image area.
Answer
k = 6 ÷ 9 = 2/3.
Image area = (2/3)² × 27 = 4/9 × 27 = 12 cm².
If you got these wrong
Congruence slips (Q1, Q2) go to recognising congruent figures. Scale factor and area slips (Q3, Q4, Q5, Q8) go to calculating enlargement scale factors.
Centre slips (Q6) go to finding the centre of enlargement. Order slips (Q7) go to describing the order of combined transformations.
If you want a teacher to go through your working, see online one-to-one Mathematics tuition.