Reflections
Objective. Reflect points and shapes in horizontal and vertical lines.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A reflection is a transformation that flips a shape over a mirror line, creating an image that is the same size and shape as the original but reversed. Every point on the reflected image is the same perpendicular distance from the mirror line as the corresponding point on the original shape, but on the opposite side. Reflecting in the line x=0 (the y-axis) keeps the y-coordinate the same but reverses the sign of the x-coordinate, so (3,2) becomes (−3,2). Reflecting in the line y=0 (the x-axis) instead reverses the sign of the y-coordinate.
Worked example
Reflect the point (4, −5) in the x-axis and state the coordinates of its image.
- 1Identify the mirror line: the x-axis, where y=0.
- 2Reflecting in the x-axis keeps the x-coordinate the same.
- 3Reverse the sign of the y-coordinate: −5 becomes 5.
- 4Write the final image coordinates.
Answer: (4, 5)
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes reflect a shape by sliding it across the page rather than flipping it, producing a translated image instead of a mirror image. Always check that the image is the same perpendicular distance from the mirror line but on the opposite side.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.