Grade 4 · Reflect a design across a vertical line · 29 of 750
Reflect a design across a vertical line: distance of marked vertex from mirror: 1
A triangular design for a classroom activity places its marked vertex 1 units left of a vertical mirror line and uses height 3. Find the reflected marked vertex's horizontal coordinate, explain the calculation, and check a related question.
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
A triangular design for a classroom activity places its marked vertex 1 units left of a vertical mirror line and uses height 3. First find the reflected marked vertex's horizontal coordinate. Then answer: How far apart are the original marked vertex and its final reflected image?
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A starting point
A reflection puts each image point on the opposite side of the mirror at the same perpendicular distance. It preserves lengths and shape while reversing orientation.
Work through the reasoning
Step 1
Identify the quantities and the task
A triangular design for a classroom activity places its marked vertex 1 units left of a vertical mirror line and uses height 3. The first task is to find the reflected marked vertex's horizontal coordinate. A reflection puts each image point on the opposite side of the mirror at the same perpendicular distance. It preserves lengths and shape while reversing orientation.
Step 2
Calculate the original result
Reflection across x = 0: (x, y) → (−x, y). The marked vertex moves from x = −1 to x = 1. Its vertical coordinate stays the same at the final image.
Step 3
Complete the follow-up calculation
How far apart are the original marked vertex and its final reflected image? 2 units: 1 to reach the mirror plus another 1 on the other side.
The answer
Reflection across x = 0: (x, y) → (−x, y). The marked vertex moves from x = −1 to x = 1. Its vertical coordinate stays the same at the final image. Follow-up: 2 units: 1 to reach the mirror plus another 1 on the other side.
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
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From experiment to screen.
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The mathematical idea
A triangular design for a classroom activity places its marked vertex 1 units left of a vertical mirror line and uses height 3. A reflection puts each image point on the opposite side of the mirror at the same perpendicular distance. It preserves lengths and shape while reversing orientation. The marked vertex moves from x = −1 to x = 1. Its vertical coordinate stays the same at the final image.
Reflection across x = 0: (x, y) → (−x, y)
03 · Reflect and transfer
Explain what changes and why.
Follow the moving triangle toward the outlined image. Compare the marked vertex's distance from the mirror before and after the motion. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
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.