12 multiple-choice questions, progressively harder.
A dilation has center OOO and scale factor 333. If OP=5OP=5OP=5 cm, how far is P′P'P′ from OOO?
Solution
Correct answer: B
Multiply the original distance by the scale factor.
OP′=3⋅5,=15 cm.\begin{aligned}OP'&=3\cdot 5,\\&=15\text{ cm}.\end{aligned}OP′=3⋅5,=15 cm.
Which description fits a dilation with scale factor 25\frac 2552?
Correct answer: D
A positive factor below one makes every distance from the center smaller.
Thus this dilation is a reduction.
A segment of length 121212 units has an image of length 888 units under a dilation. What is the scale factor?
Correct answer: A
Put the image length over the original length.
k=812,=23.\begin{aligned}k&=\frac 8{12},\\&=\frac 23.\end{aligned}k=128,=32.
An angle measures 117∘117^\circ117∘. A dilation has scale factor 222. What is the image angle measure?
Correct answer: C
A dilation preserves angle measures. It does not multiply them by its length factor.
Where does (−2,7)(-2, 7)(−2,7) map under a dilation centered at the origin with scale factor 222?
The center is the origin, so multiply both coordinates by two.
Which points are fixed under a dilation with scale factor 111?
A fixed point maps to itself. With scale factor 111, every displacement from the center stays the same, so every point is fixed.
A dilation has scale factor 444. Which statement about its fixed points is true?
The center stays at distance zero from itself. Every other point has its positive distance from the center multiplied by four, so it moves.
A line passes through the center of a dilation with positive scale factor. What is its image?
Every point on the line maps along one of the two rays of that line from the center. Every location on the line is reached by an image, so the whole line maps onto itself as a set.
A dilation has scale factor 0.60.60.6. A line does not pass through its center. What is the image line?
Since the factor is positive and different from one, the accepted line-image property gives a distinct parallel image for a line away from the center.
A transformation triples horizontal lengths but leaves vertical lengths unchanged. Why is it not a dilation?
One dilation uses one length factor for every segment. A factor of three horizontally and one vertically cannot be the same factor.
For a dilation with center OOO and scale factor 12\frac 1221, where is the image of a point P≠OP\ne OP=O?
The positive factor keeps the image on the same ray and halves its distance from the center.
A dilation has center (3,−2)(3,-2)(3,−2) and scale factor 0.40.40.4. Where does the center itself map?
The center maps to itself under every dilation. The factor acts on displacements from that center, and the center has zero displacement.
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