Ten multiple-choice questions check scale factor, dilations on the coordinate plane, lines under dilation and the AA criterion. Pick the single best answer for each question, then read the explanation to learn the typical mistake.
GeometryCommon Core: G-SRT.A.1 · G-SRT.A.2 · G-SRT.A.3
🎯 Dilations and Similarity Transformations – Geometry math quiz
Question 1
Which statement is true for every dilation?
A
Every point moves the same distance
B
Every point stays the same distance from the center
C
Every point moves to the other side of a line
D
The center does not move
Question 2
A dilation with center O maps P to \(P^{\prime}\). \(OP=4\) in. and \(OP^{\prime}=10\) in. What is the scale factor?
A
\(\frac{2}{5}\)
B
\(\frac{5}{2}\)
C
\(6\)
D
\(\frac{7}{2}\)
Question 3
Point A is dilated about the origin O with scale factor 2. What are the coordinates of \(A^{\prime}\)?Point A(2, 3) and the center O.
A
\((4,6)\)
B
\((4,5)\)
C
\((1,1.5)\)
D
\((6,9)\)
Question 4
Which scale factor produces a reduction?
A
\(\frac{4}{3}\)
B
\(\frac{3}{4}\)
C
\(1\)
D
\(\frac{7}{6}\)
Question 5
A dilation about the origin has scale factor 3. What is the image of the line \(y=2x-6\)?
A
\(y=6x-18\)
B
\(y=2x-2\)
C
\(y=2x-18\)
D
\(y=2x-6\)
Question 6
A 12 cm segment is dilated with scale factor \(\frac{5}{6}\). How long is the image?
A
14.4 cm
B
10 cm
C
12 cm
D
17 cm
Question 7
Are the two triangles similar?Two angles are marked in each triangle.
A
No, only one angle pair matches
B
No, side lengths are needed
C
No, the triangles face different ways
D
Yes, both have angles 40, 55 and 85 degrees
Question 8
A triangle with a \(72^{\circ}\) angle is dilated with scale factor \(\frac{1}{4}\). What is the measure of the matching image angle?
A
18 degrees
B
288 degrees
C
72 degrees
D
36 degrees
Question 9
A dilation has center \(C(1,1)\) and scale factor 2. What is the image of \(P(4,3)\)?
A
\((7,5)\)
B
\((8,6)\)
C
\((9,7)\)
D
\((2.5,2)\)
Question 10
In the figure, \(OA=3\) and \(AA^{\prime}=6\). What is the scale factor of the dilation with center O?A dilation with center O maps A to A′.
A
\(3\)
B
\(2\)
C
\(9\)
D
\(\frac{1}{3}\)
🎉 Quiz complete!
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Remember:
- A dilation needs a center and a positive scale factor k; the center never moves (G-SRT.A.1).
- A line through the center maps to itself; any other line maps to a parallel line, and every segment is multiplied by k.
- About the origin, a dilation is (x, y) to (kx, ky); angle measures stay the same.
- Figures are similar when a sequence of rigid motions and dilations maps one onto the other (G-SRT.A.2).
- AA criterion: two pairs of congruent angles are enough to prove triangles similar (G-SRT.A.3).
See every chapter on the Geometry math page.