Vector notation and translations Worked Solutions — GCSE Maths

Write the translation as a coordinate rule

Translating by $\begin{pmatrix} 4 \\ 3 \end{pmatrix}$ adds $4$ to every $x$-coordinate and $3$ to every $y$-coordinate.

Apply the rule to P

Adding the vector to the coordinates of $P(2, 1)$ gives $P'(6, 4)$.

State the coordinates of the image

The image of $P(2, 1)$ under the translation $\begin{pmatrix} 4 \\ 3 \end{pmatrix}$ is $P'(6, 4)$.

Write the translation as a coordinate rule

Translating by $\begin{pmatrix} -5 \\ 1 \end{pmatrix}$ adds $-5$ to every $x$-coordinate and $1$ to every $y$-coordinate.

Apply the rule to P

Adding the vector to the coordinates of $P(3, 2)$ gives $P'(-2, 3)$.

State the coordinates of the image

The image of $P(3, 2)$ under the translation $\begin{pmatrix} -5 \\ 1 \end{pmatrix}$ is $P'(-2, 3)$.

Write the translation as a coordinate rule

Translating by $\begin{pmatrix} 2 \\ -6 \end{pmatrix}$ adds $2$ to every $x$-coordinate and $-6$ to every $y$-coordinate.

Apply the rule to Q

Adding the vector to the coordinates of $Q(1, 4)$ gives $Q'(3, -2)$.

State the coordinates of the image

The image of $Q(1, 4)$ under the translation $\begin{pmatrix} 2 \\ -6 \end{pmatrix}$ is $Q'(3, -2)$.

Write the translation as a coordinate rule

Translating by $\begin{pmatrix} -3 \\ -4 \end{pmatrix}$ adds $-3$ to every $x$-coordinate and $-4$ to every $y$-coordinate.

Apply the rule to R

Adding the vector to the coordinates of $R(-2, 3)$ gives $R'(-5, -1)$.

State the coordinates of the image

The image of $R(-2, 3)$ under the translation $\begin{pmatrix} -3 \\ -4 \end{pmatrix}$ is $R'(-5, -1)$.

Write the translation as a coordinate rule

Translating by $\begin{pmatrix} -4 \\ 2 \end{pmatrix}$ adds $-4$ to every $x$-coordinate and $2$ to every $y$-coordinate.

Apply the rule to P

Adding the vector to the coordinates of $P(0, 0)$ gives $P'(-4, 2)$.

State the coordinates of the image

The image of $P(0, 0)$ under the translation $\begin{pmatrix} -4 \\ 2 \end{pmatrix}$ is $P'(-4, 2)$.