110
Symmetry across a line
Textbook: Part 4, lesson 110, pp. 7–9
GoalSymmetry across a line (reflection): constructing a symmetric point and segment.
New words
reflection symmetry · aks simmetriyaperpendicular · perpendikulardistance · masofasymmetric point · simmetrik nuqta
Explanation
To construct the point B symmetric to A across an axis: a) draw a line from A perpendicular to the axis; b) measure the distance from A to the axis; c) mark B on the other side of the axis at the same distance. A point on the axis is symmetric to itself. To make a symmetric segment, construct points symmetric to its ends and join them. Symmetric segments have equal length.
Worked examples
The vertical axis is x = 4. Point A(1; 3) is 3 squares left of the axis, so its symmetric point is 3 squares to the right: (7; 3).
The horizontal axis is y = 5. B(2; 8) is 3 squares above the axis, so its symmetric point is 3 squares below: (2; 2).
Class activity
“Mirror game”: in pairs, one child draws points and segments on squared paper and the other draws the picture symmetric across an axis. Then they fold to check.
Practice
1
The vertical axis of symmetry is x = 4. Write the coordinates of the point symmetric to A(1; 3).
(7; 3)
2
The horizontal axis is y = 5. Write the coordinates of the point symmetric to B(2; 8).
(2; 2)
3
Point C is 6 cm from the axis of symmetry. How many centimetres is it from its symmetric point?
12
4
Segment AB is 7 cm long. How long in centimetres is the segment A1B1 symmetric to it across an axis?
7
5
Which point is symmetric to a point lying on the axis of symmetry?
the point itself