Translations and Reflections
Grade 4Translations
A translation slides a shape without rotating or reflecting it. Every point moves the same distance in the same direction. Translations are described using a column vector: the top number is horizontal movement (positive = right) and the bottom is vertical (positive = up).
To describe a translation fully, just state the column vector. Do not say "3 right and 2 down" — write it as (3, −2). That is the precise notation expected in the exam.
Reflections
A reflection flips a shape over a mirror line. Every point in the image is the same perpendicular distance from the mirror as the original. Describe a reflection by stating the equation of the mirror line.
Common mirror lines to know: x = 0 (the y-axis), y = 0 (the x-axis), y = x, y = −x, and any vertical (x = k) or horizontal (y = k) line.
Worked example
EXAMPLE
Point A is at (3, 5). It is translated by (−4, 2) to give A'. Then A' is reflected in the line y = x to give A''. Find the coordinates of A''.
After translation: A' = (3 + (−4), 5 + 2) = (−1, 7). Reflection in y = x swaps coordinates: A'' = (7, −1).
