Reflections Flashcards

All 6 cards in this deck

On a coordinate grid, what do the mirror lines $x=3$ and $y=-2$ look like?

$x=3$ is a vertical line through $(3,0)$; $y=-2$ is a horizontal line through $(0,-2)$.

On a coordinate grid, what do the mirror lines $y=x$ and $y=-x$ look like?

Both are diagonal lines through the origin: $y=x$ has gradient $1$ (through $(1,1)$), $y=-x$ has gradient $-1$ (through $(1,-1)$).

What must you state to describe fully a reflection?

Reflection, and the equation of the mirror line, e.g. reflection in the line $x=-1$.

What are the steps to reflect a shape in a given mirror line?

e.g. reflect in the line $y=x$

1. Measure the perpendicular distance from a vertex to the mirror line.
2. Plot the image vertex the same distance on the other side, on that perpendicular.
3. Repeat for all vertices and join them; for $y=x$ each point $(x,y)$ lands at $(y,x)$.

True or false? Any point lying on the mirror line is invariant under the reflection.

True. Points on the mirror line map onto themselves.

A graph sketched on axes is reflected in the $x$-axis. What happens to the coordinates of each point?

$(x,y)\to(x,-y)$ — the $x$-coordinate stays the same and the $y$-coordinate changes sign.