Symmetry (Including Reflection and Rotation)
ICSE · Class 8 · Mathematics
Flashcards for Symmetry (Including Reflection and Rotation) — ICSE Class 8 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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A plane figure is folded about a line on it and the two parts exactly coincide. What is this property called?
Answer
Step 1: Check what happens on folding the figure. Step 2: If both parts exactly coincide, the figure has symmetry. Answer: A plane figure is said to have symmetry, also called linear symmetry.
A figure is symmetrical about a line. What is that line called?
Answer
The line about which the figure is symmetrical is called a line of symmetry, an axis of symmetry, or simply a mirror line.
When a point P(x, y) is reflected in the x-axis, what is the image point? Give the formula and one example using P(4, 7).
Answer
Formula: Reflection in x-axis: P(x, y) → P'(x, -y) Step 1: Keep x the same. Step 2: Change the sign of y. For P(4, 7), the image is P'(4, -7). Answer: P'(x, -y), so P(4, 7) becomes (4, -7).
Find the reflection of the point (-6, 9) in the x-axis.
Answer
Step 1: Use the rule for reflection in x-axis: P(x, y) → P'(x, -y) Step 2: Keep x = -6 the same. Step 3: Change 9 to -9. Answer: (-6, -9)…
Find the reflection of the point (8, -5) in the x-axis.
Answer
Step 1: Use P(x, y) → P'(x, -y) Step 2: Keep x = 8 the same. Step 3: Change -5 to 5. Answer: (8, 5)…
When a point P(x, y) is reflected in the y-axis, what changes? Use P(-3, 11) as an example.
Answer
Formula: Reflection in y-axis: P(x, y) → P'(-x, y) Step 1: Change the sign of x. Step 2: Keep y the same. For P(-3, 11), the image is P'(3, 11). Answer: Only the x-coordinate changes sign.
Find the reflection of the point (7, -4) in the y-axis.
Answer
Step 1: Use P(x, y) → P'(-x, y) Step 2: Change 7 to -7. Step 3: Keep -4 the same. Answer: (-7, -4)…
Find the reflection of the point (0, 9) in the y-axis.
Answer
Step 1: Use P(x, y) → P'(-x, y) Step 2: Change the sign of x. Step 3: Since x = 0, the point stays on the y-axis. Answer: (0, 9)…
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