Topics › KS3 › Geometry & measures

Transformations

1. tr-01 Present from here

   The point $(2, 4)$ is translated by the vector $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$. Where does it end up?

   A Option A: $(0, 7)$

   B Option B: $(5, 6)$

   C Option C: $(5, 2)$

   D Option D: $(-1, 6)$
   Answer and misconceptions

   A Option A: $(0, 7)$ ✗

   Reads the vector the wrong way roundMoves −2 in x and 3 in y; the top number is the horizontal move.

   B Option B: $(5, 6)$ ✗

   Ignores the negative sign in the vectorMoves up 2 instead of down 2.

   C Option C: $(5, 2)$ ✓ Correct

   D Option D: $(-1, 6)$ ✗

   Translates in the opposite directionSubtracts the vector: moves left 3 and up 2.
2. tr-02 Present from here

   The point $(1, 4)$ is reflected in the line $x = 3$. Where is its image?

   A Option A: $(5, 4)$

   B Option B: $(1, 2)$

   C Option C: $(-1, 4)$

   D Option D: $(4, 1)$
   Answer and misconceptions

   A Option A: $(5, 4)$ ✓ Correct

   B Option B: $(1, 2)$ ✗

   Thinks x = 3 is a horizontal lineReflects in y = 3; the line x = 3 is vertical.

   C Option C: $(-1, 4)$ ✗

   Reflects in the y-axis insteadIgnores the given mirror line and just changes the sign of x.

   D Option D: $(4, 1)$ ✗

   Swaps the coordinatesSwapping x and y reflects in y = x, not in x = 3.
3. tr-03 Present from here

   The point $(3, 1)$ is rotated $90^\circ$ clockwise about the origin. Where is its image?

   A Option A: $(-1, 3)$

   B Option B: $(-3, -1)$

   C Option C: $(1, 3)$

   D Option D: $(1, -3)$
   Answer and misconceptions

   A Option A: $(-1, 3)$ ✗

   Rotates anticlockwise instead of clockwise(−1, 3) is the result of a 90° anticlockwise turn.

   B Option B: $(-3, -1)$ ✗

   Rotates 180° instead of 90°Changes both signs, which is a half turn.

   C Option C: $(1, 3)$ ✗

   Swaps coordinates without changing a signSwapping alone is a reflection in y = x, not a rotation.

   D Option D: $(1, -3)$ ✓ Correct
4. tr-04 Present from here

   Point $P$ is enlarged by scale factor $2$, centre $Q$. What are the coordinates of the image of $P$?

   
   A Option A: $(6, 4)$

   B Option B: $(5, 3)$

   C Option C: $(5, 4)$

   D Option D: $(7, 4)$
   Answer and misconceptions

   A Option A: $(6, 4)$ ✗

   Enlarges from the origin, ignoring the centreDoubles the coordinates of P instead of doubling its distance from Q.

   B Option B: $(5, 3)$ ✓ Correct

   C Option C: $(5, 4)$ ✗

   Adds the scale factor to each coordinateAdds 2 to x and y instead of multiplying the distance from Q by 2.

   D Option D: $(7, 4)$ ✗

   Measures the doubled distance from P, not QDoubles the move from Q to P to get 4 right, 2 up, but counts it from P instead of from Q.
5. tr-05 Present from here

   Which vector describes the translation from shape P to shape Q?

   
   A Option A: $\begin{pmatrix} 2 \\ 3 \end{pmatrix}$

   B Option B: $\begin{pmatrix} -3 \\ -2 \end{pmatrix}$

   C Option C: $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$

   D Option D: $\begin{pmatrix} 4 \\ 3 \end{pmatrix}$
   Answer and misconceptions

   A Option A: $\begin{pmatrix} 2 \\ 3 \end{pmatrix}$ ✗

   Writes the vector with x and y swappedThe top number is the horizontal move (3 right), the bottom the vertical (2 up).

   B Option B: $\begin{pmatrix} -3 \\ -2 \end{pmatrix}$ ✗

   Describes the move from Q back to PReverses the direction; P to Q is right and up, so both are positive.

   C Option C: $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ ✓ Correct

   D Option D: $\begin{pmatrix} 4 \\ 3 \end{pmatrix}$ ✗

   Gives a coordinate of Q, not the movement(4, 3) is where a corner of Q is; the vector is how far each point moves.