A reliable method
Apply coordinate rules to one point at a time and label the transformation centre or mirror line. Add corresponding vector components.
The common trap
A rotation needs a direction, angle and centre. Reflecting in the y-axis changes x, not y.
Make the connection
Test a transformation with a simple point and check whether distances are preserved. A vector describes displacement rather than an absolute location.
Track a point through the stated transformation
Reflecting (3,−2) in the y-axis gives (−3,−2); reflecting it in the x-axis instead gives (3,2). A 90-degree anticlockwise rotation about the origin maps (x,y) to (−y,x), so (2,5) becomes (−5,2). Merely changing signs produces a half-turn, not a quarter-turn. For vectors u=(3,1) and v=(4,−2), compute 2u−v=(6,2)−(4,−2)=(2,4). The minus sign applies to both components of v. A vector describes displacement, while a point specifies a location.
Transfer, explain and check
Translate (−1,4) by (3,−2) to get (2,2), then rotate it 90 degrees anticlockwise to get (−2,2). Reverse the order and compare: rotation gives (−4,−1), then translation gives (−1,−3). Order matters.
Point (3,−2) is translated by vector (−5,3). What is its new x-coordinate?
- A translation adds each displacement component.
- Only the first component changes x.
- Subtract 5 from the original x-coordinate.
Compare the other answer choices
Apply the vertical displacement to the x-coordinate.
Subtract the displacement instead of adding its signed value.
Return the displacement rather than the translated coordinate.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Cambridge IGCSE Mathematics 0580