Move a Point by a Translation Vector
A translation adds the same horizontal and vertical displacements to every point.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: Translate (-2,3) by vector (3,−2). Candidate answers: (A) (-5,5) (B) (-6,-6) (C) (1,1) (D) (1,5).
- Independent check inputs: Translate (-3,4) by vector (3,−2). Candidate answers: (A) (-6,6) (B) (-9,-8) (C) (0,2) (D) (0,6).
Learn the idea
Translations, reflections and rotations preserve distances and angle measures. Coordinate rules describe these moves exactly, and a sequence of moves must be applied in its stated order to determine the final image. A translation adds the same horizontal and vertical displacements to every point. Its coordinate differences remain unchanged, so a translated figure retains both size and orientation.
Here is the method on the supplied teaching case. Add each component to the matching coordinate: (-2+3,3−2)=(1,1). Translation preserves lengths and angle measures.
Add vector components to matching coordinates; do not multiply them or reverse signs without a reason. A negative vertical displacement moves downward in the stated Cartesian coordinate convention.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: Translate (-2,3) by vector (3,−2). Candidate answers: (A) (-5,5) (B) (-6,-6) (C) (1,1) (D) (1,5). Solution: Add each component to the matching coordinate: (-2+3,3−2)=(1,1). Translation preserves lengths and angle measures. The final answer is (1,1). Add vector components to matching coordinates; do not multiply them or reverse signs without a reason. A negative vertical displacement moves downward in the stated Cartesian coordinate convention.
Check your reasoning
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Helpful tips
- A translation adds the same horizontal and vertical displacements to every point.
- Add vector components to matching coordinates; do not multiply them or reverse signs without a reason.
See the answer and explanation
(0,2)
Add each component to the matching coordinate: (-3+3,4−2)=(0,2). Translation preserves lengths and angle measures.
Take it further
Changed-input task: Translate (-9,10) by vector (3,−2). Candidate answers: (A) (-12,12) (B) (-27,-20) (C) (-6,12) (D) (-6,8). Show the mathematical reason, not only the selected answer. Expected result: (-6,8). Add each component to the matching coordinate: (-9+3,10−2)=(-6,8). Translation preserves lengths and angle measures.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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