Symmetry and the Cartesian Plane | Form 1 Mathematics

Symmetry and the Cartesian Plane

Symmetry describes balanced figures, while the Cartesian plane gives a precise way to locate and connect points.

Symmetry

A point reflection in a centre places the image the same distance on the opposite side. A figure has line symmetry when a line divides it into matching mirror halves. A figure may have more than one line of symmetry.

Cartesian plane

The horizontal axis is the x-axis and the vertical axis is the y-axis. They meet at the origin (0,0). A point is written (x,y): move x units horizontally, then y units vertically.

Worked examples

1. The reflection of (3,2) in the origin is (−3,−2).
2. The reflection of (4,−1) in the y-axis is (−4,−1), while reflection in the x-axis is (4,1).
3. Join plotted points in order to form a figure, then inspect whether a mirror line maps each vertex to another vertex.

Practice

1. Plot (2,3), (−2,3), (−2,−1) and (2,−1). What shape is formed?
2. Reflect (5,−2) in each coordinate axis.
3. Find the lines of symmetry of a square, rectangle and equilateral triangle.