10A

Reflections and translations

Reflecting points and shapes in the x-axis, y-axis and other lines, and translating them by a given number of units across and up or down.

Reflections

Reflecting a point

Drag P. Each image is the same distance from the mirror line as P, on the other side.

Example 1●

Reflect $(3, -2)$ in the $x$-axis and in the $y$-axis.

$x$-axis: $(3, 2)$

$y$-axis: $(-3, -2)$

A translation slides every point the same distance in the same direction. "$3$ right, $5$ down" adds $3$ to $x$ and subtracts $5$ from $y$.

Example 2●

Translate $(1, 4)$ by $3$ units right and $5$ units down.

$(1 + 3, 4 - 5) = (4, -1)$

Flashcards

Reflect in $x$-axis

$(x, y) \to (x, -y)$

Reflect in $y$-axis

$(x, y) \to (-x, y)$

Translate 2 left, 1 up

$(x, y) \to (x - 2, y + 1)$

Practice

Reflect $(3, -2)$ in the $x$-axis. Enter $x, y$.
Reflect $(3, -2)$ in the $y$-axis.
Translate $(1, 4)$ by $3$ right and $5$ down.
Translate $(-2, 3)$ by $3$ left and $3$ up.
Reflect $(0, 4)$ in the $x$-axis.
Reflect $(-5, 0)$ in the $y$-axis.
$(2, 7)$ moves to $(6, 4)$. The translation is:
A reflected shape is: