Reflection — Part 1: Images in the axes, the origin and lines parallel to the axes: visual lesson, ICSE Class 10 Mathematics

Lesson

Reflection, Part 1

A reflection makes a mirror image: every point moves to the other side of a mirror line, the same distance away. On a graph the coordinates of the image follow simple rules.

In this lesson you will

Describe a reflection: the mirror line is the perpendicular bisector of a point and its image
Write the image of a point reflected in the x-axis, the y-axis or the origin
Write the image of a point reflected in a line x = a or y = b
Work backwards to find a point, a mirror line or unknown coordinates

triangle ABC
image A′B′C′

Each vertex of the image is as far behind the mirror as the vertex is in front of it.

Concept

What you will be able to do

Explain what a reflection does to a point
Reflect a point in the $x$ -axis, the $y$ -axis and the origin
Reflect a point in a line $x = a$ or $y = b$
Find a point, a mirror line or unknown coordinates from given images

Concept

What a reflection does

The image $P'$ of a point $P$ in a mirror line lies on the other side of the line, so that the mirror is the perpendicular bisector of $PP'$ .

$PP'$ crosses the mirror at right angles
the mirror cuts $PP'$ in half: $P$ and $P'$ are the same distance from it
a point on the mirror is its own image: it is invariant

PP′

The mirror is the perpendicular bisector of $PP'$: $PM = MP' = 2$.

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