Discover Mathematics P4: Term 2, Unit 12, Lessons 6–10
GoalComplete a symmetrical picture on squared paper by drawing the mirror image across a line.
New words
mirror line · the line of symmetry, like a mirror, between a shape and its imageimage · the reflected copy of a shape on the other side of the mirror linesymmetrical · having two halves that match exactly when folded along a line
Explanation
A symmetrical picture has two halves that are mirror images of each other. To finish a picture when you are given one half and the mirror line, draw each point of the half again on the other side of the line. Every point and its image are the same distance from the mirror line, and the segment joining them is perpendicular to the line. On squared paper this is easy: count how many squares a corner is from the line, then count the same number of squares on the other side, at the same height. Do this for every corner and join the corners in the same order. The corners that lie on the mirror line stay where they are. The finished figure can be folded along the mirror line into two matching halves.
Worked examples
Here is half a shape to the right of the dashed mirror line. Its corners are 3 squares, 3 squares and 1 square away from the line. We draw the corners 3, 3 and 1 squares to the left of the line, at the same heights, and join them. The whole figure then has two matching halves.
Find the image of the point M. M is 2 squares to the right of the mirror line and 1 square up. Its image is 2 squares to the left of the line and 1 square up. A point and its image are the same distance from the line, on opposite sides.
A mirror line can also be horizontal. Here the half of a house is above the line. A corner 3 squares above the line has its image 3 squares below the line. The figure is 3 + 3 = 6 squares tall once it is complete, and 4 squares wide.
Class activity
Butterfly. Fold a sheet of paper in half and draw half of a butterfly with its middle on the fold. Cut it out along your line while the paper is folded and open it up. Is the butterfly symmetrical? Where is its line of symmetry? Now draw half of another picture on squared paper and ask a friend to finish it.
Practice
1
A corner is 3 squares to the right of a vertical mirror line. Where is its image?
3 squares to the left of the line, at the same height.
2
A corner is 4 squares above a horizontal mirror line. Where is its image?
4 squares below the line, directly under the corner.
3
The half of a figure is 5 squares wide from the mirror line. How wide is the whole figure?
5 + 5 = 10 squares wide.
4
Name three things at home or in nature with a line of symmetry.
For example: a butterfly, a leaf, a door, a plate.
5
Salma says the image of a corner is on the same side of the mirror line as the corner. Is she right?
No. The image is on the opposite side of the mirror line, at the same distance.
