Congruency, Enlargement and Combined Transformations · Form 5
Congruency, Enlargement and Combined Transformations: Worked Examples (Easier)
Covers the basics of single transformations, translating a point, reflecting a point in an axis, and using area = k² × object area for a simple enlargement. Best for students building confidence before combined problems.
Worked example 1
The point A(−2, 5) is moved by a translation of 7 units to the right and 3 units down (vector (7, −3), where positive means right and up). Find the coordinates of the image A′.
- A translation adds the vector's components to the point's coordinates.
- New x-coordinate: −2 + 7 = 5.
- New y-coordinate: 5 + (−3) = 2.
Worked example 2
The point B(4, −3) is reflected in the y-axis. Find the coordinates of the image B′.
- Reflection in the y-axis reverses the sign of the x-coordinate and keeps y unchanged: (x, y) → (−x, y).
- x-coordinate: −(4) = −4.
- y-coordinate stays −3.
Worked example 3
A rectangle has an area of 8 cm². It undergoes an enlargement with scale factor 4.
Find the area of the image.
- For an enlargement, area of image = k² × area of object.
- Square the scale factor: k² = 4² = 16.
- Area of image = 16 × 8 = 128 cm².
Worked example 4
Point A(−3, 2) is reflected in the x-axis. State the coordinates of the image.
- Reflection in the x-axis: (x, y) → (x, −y)
- A(−3, 2) → (−3, −2)
Worked example 5
Point B(3, 1) is rotated 90° clockwise about the origin O. State the coordinates of the image.
- Rotation 90° clockwise about O: (x, y) → (y, −x)
- B(3, 1) → (1, −3)
Worked example 6
A triangle of area 6 cm² undergoes an enlargement with scale factor 3. Calculate the area of the image.
- Area scale factor = k² = 3² = 9
- Image area = 9 × 6 = 54 cm²
Worked example 7
Point C(5, −2) is translated by the vector (−4, 6), that is, 4 units to the left and 6 units up. Find the coordinates of the image C′.
- x-coordinate of image = 5 + (−4) = 1
- y-coordinate of image = −2 + 6 = 4
Worked example 8
Point D(−3, 5) is rotated 90° anticlockwise about the origin O. State the coordinates of the image D′.
- For a 90° anticlockwise rotation about the origin, (x, y) → (−y, x)
- D(−3, 5) → D′(−5, −3)
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What basic skills do easy questions on this topic check?
Easy questions test whether you can identify congruent shapes by comparing corresponding sides and angles, and whether you can describe or perform a simple enlargement, stating the centre of enlargement and scale factor, and finding the image of a point or shape under that enlargement.
What is a common mistake when finding the scale factor?
Students often calculate the scale factor the wrong way round, dividing the object's length by the image's length instead of image over object (or vice versa depending on convention), which flips whether the enlargement is a magnification or reduction. Always check which shape is the object and which is the image first.
How should students state the centre of enlargement clearly?
Give the centre as a coordinate point (or describe its position if coordinates aren't used) and check it by confirming that lines joining corresponding points on the object and image all pass through that same point. Just estimating the centre by eye without checking with at least one pair of points can lead to an incorrect answer.