Online Test — Transformations
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
Which geometric transformation can be perfectly described using only a column vector?
Reflection
Translation
Rotation
Enlargement
Explanation: A translation slides points by a fixed horizontal and vertical vector shift.
Question 2 of 10
If point \(P(2, 7)\) is translated by vector \(\begin{pmatrix} -3 \\ 1 \end{pmatrix}\), what are the new coordinates?
\((5, 8)\)
\((-1, 8)\)
\((-1, 6)\)
\((5, 6)\)
Explanation: \(x' = 2 + (-3) = -1\) and \(y' = 7 + 1 = 8\). Coordinates are \((-1, 8)\).
Question 3 of 10
Reflecting the point \(M(4, -5)\) across the \(x\)-axis outputs which coordinate pair?
\((-4, -5)\)
\((4, 5)\)
\((-4, 5)\)
\((5, 4)\)
Explanation: Under reflection across the \(x\)-axis, \((x, y) \rightarrow (x, -y)\). So \((4, -5) \rightarrow (4, 5)\).
Question 4 of 10
How many total lines of symmetry can be drawn inside a standard rectangle?
1
2
4
Infinite
Explanation: A rectangle can be folded perfectly across its horizontal and vertical mid-lines.
Question 5 of 10
What is the order of rotational symmetry for a regular square?
1
2
4
8
Explanation: A square looks identical four times during a \(360^\circ\) rotation.
Question 6 of 10
Calculate the minimum rotation angle needed for a regular pentagon to match its starting look.
\(45^\circ\)
\(60^\circ\)
\(72^\circ\)
\(90^\circ\)
Explanation: Order is \(5\). \(\text{Angle} = 360^\circ \div 5 = 72^\circ\).
Question 7 of 10
An object length of \(5\text{ cm}\) becomes an image length of \(20\text{ cm}\). Find the scale factor \(k\).
\(k = 0.25\)
\(k = 2\)
\(k = 4\)
\(k = 15\)
Explanation: \(k = \text{Image} \div \text{Object} = 20 \div 5 = 4\).
Question 8 of 10
Which transformation can alter the physical size of the geometric shape?
Reflection
Translation
Rotation
Enlargement
Explanation: Enlargement scales side lengths, making shapes larger or smaller.
Question 9 of 10
If a shape is rotated \(180^\circ\) around the origin, the point \((x, y)\) maps onto:
\((y, x)\)
\((-x, y)\)
\((x, -y)\)
\((-x, -y)\)
Explanation: A half-turn rotation flips the positive/negative signs of both coordinates.
Question 10 of 10
If a shape is enlarged by a scale factor of \(k = 3\), its interior area increases by:
\(3\) times
\(6\) times
\(9\) times
\(27\) times
Explanation: Area scales by the square of the factor: \(k^2 = 3^2 = 9\).