Reflections
🎯 In this topic you will
- Reflect 2D shapes in horizontal, vertical and diagonal mirror lines.
🧠 Key Words
- diagonal mirror line
Show Definitions
- diagonal mirror line: A slanted line across a shape where each point on one side has a matching reflected point on the opposite side.
Seeing Reflections Around Us
What do you see when you look in a mirror? You see a reflection of yourself and the world around you. Artists use reflections in their paintings. Even the very earliest artists noticed that shiny objects, water, or even a person’s eyes could show a reflection, and they tried to include these in their artworks to make them look as realistic as possible.
Using Reflections in Art
When you next draw a picture, try to include a reflection. Remember that in a piece of art it does not always have to be a perfect or true reflection. Artists sometimes change reflections slightly to make their pictures more interesting or creative.
❓ EXERCISES
$1.$ Which drawings show correct reflections of triangle $A$?
👀 Show answer
$2.$ Copy each diagram and reflect the shape in the horizontal and vertical mirror lines.
👀 Show answer
🧠 Think like a Mathematician
This is part of Arun’s homework.
Question: Reflect shape $A$ in the diagonal line of symmetry. Label your answer shape $B$.
This is the method that Arun uses:
- Trace shape $A$ and the mirror line using tracing paper.
- Turn the tracing paper until the mirror line on the tracing paper fits exactly over the mirror line on the diagram.
- Observe where the reflected shape appears and mark this position.
- Draw the reflected shape and label it $B$.
Follow-up Questions:
Show Answers
- a: Shape $B$ is not drawn correctly because the reflected shape must be the same perpendicular distance from the mirror line as shape $A$. Some vertices of $B$ are not placed at equal distances across the diagonal line.
- b: Arun’s tracing method is reasonable because reflections can be checked by folding or tracing. However, the mirror line must align perfectly, and each vertex must be placed at the same distance on the opposite side of the mirror line. Measuring distances on the grid helps ensure accuracy.
- c: A correct reflection keeps the shape the same size and shape while placing every point the same distance from the mirror line on the opposite side. Checking each vertex individually helps confirm the reflection is accurate.
❓ EXERCISES
$3.$ Copy each diagram and reflect the shape in the diagonal mirror lines. The first one has been started for you.
👀 Show answer
$4.$
$a.$ Describe the mirror line for each of these reflections.
$b.$ Copy each diagram in part $a$ and draw in the correct mirror line for each reflection.
👀 Show answer
$i$ horizontal mirror line.
$ii$ vertical mirror line.
$iii$ diagonal mirror line.
b. Draw the mirror line halfway between each pair of corresponding points of the original shape and its reflection.
🧠 Think like a Mathematician
Work on this activity on your own.
Task: On a piece of squared paper, make a copy of the grid and the diagonal mirror line.
Method:
- Draw a quadrilateral inside the shaded region of the grid.
- Reflect the quadrilateral across the diagonal mirror line.
- Check that each vertex of the reflected shape is the same perpendicular distance from the mirror line as the original vertex.
- Compare the reflected shape with the original to make sure the size and shape are unchanged.
- If any points are not correct, adjust the reflected vertices and redraw the shape.
Reflection Questions:
Show Answers
- 1: Measure the perpendicular distance from each vertex to the mirror line and make sure the reflected vertex is the same distance on the opposite side.
- 2: The size, shape, and distances between points stay the same; only the orientation changes.
- 3: The mirror line must lie exactly halfway between corresponding points so that the reflection is symmetrical on both sides.
💡 Quick Math Tip
Using Tools to Check Reflections: If you are unsure about a reflection, place tracing paper over the diagram or use a small mirror along the mirror line. This helps you see exactly where the reflected shape should appear.