Grade 8 · Translate every coordinate equally · 542 of 750
Translate every coordinate equally · practice 61
Translate the point (1, 1) by the vector (1, -3). Find the image and the movement length. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Translate the point (1, 1) by the vector (1, -3). Find the image and the movement length.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Add corresponding coordinates; use both displacement components for distance.
Work through the reasoning
Step 1
Translate the givens
Horizontal displacement is 1; vertical displacement is -3. They are added independently.
Step 2
Calculate with the model
The image is (1 + (1), 1 + (-3)) = (2, -2).
Step 3
Check and interpret
Movement length = √((1)² + (-3)²) = √10 ≈ 3.16228. Subtracting the vector restores (1,1).
The answer
Image = (2, -2); length = √10 ≈ 3.16228.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
The mathematical idea
A translation adds one displacement vector to every point of a figure. Corresponding sides remain parallel and equal, so shape and size are preserved. The movement's length comes from its horizontal and vertical components, not from adding those components directly. Starting quantities: Horizontal displacement = 1; Vertical displacement = -3.
(x,y) ↦ (x+u,y+v)
03 · Reflect and transfer
Explain what changes and why.
Why can a negative displacement component still contribute a positive square to distance?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.