Dilations and Similarity Transformations: Geometry Math Test – PDF Download

Question 1: Scale factor and image lengths (2 points)

A dilation with center O maps A to \(A^{\prime}\) and B to \(B^{\prime}\). In the figure, \(OA=5\) cm, \(OA^{\prime}=12.5\) cm, \(OB=4\) cm and \(AB=3\) cm.

1. Find the scale factor. (1 point)
2. Find \(A^{\prime}B^{\prime}\). (1 point)

Question 2: Dilate points about the origin (2 points)

Dilate each point about the origin with the given scale factor and write the image.

1. \(P(4,-6),\ k=\frac{3}{2}\) (1 point)
2. \(Q(-10,15),\ k=0.4\) (1 point)

Question 3: Dilate a triangle on the plane (3 points)

Triangle ABC is graphed. It is dilated about the origin with scale factor 2 to form \(A^{\prime}B^{\prime}C^{\prime}\).

1. Find the coordinates of the three image vertices. (1 point)
2. Find \(BC\) and \(B^{\prime}C^{\prime}\). (1 point)
3. Show that \(BC\) and \(B^{\prime}C^{\prime}\) are parallel. (1 point)

Question 4: Dilating a line (2 points)

Both lines are dilated about the origin with scale factor 4. Write an equation of each image.

1. \(y=-2x+3\) (1 point)
2. \(y=3x\) (1 point)

Question 5: Center other than the origin (2 points)

A dilation has center \(C(2,1)\) and scale factor 3. Find the image of each point.

1. \(A(4,3)\) (1 point)
2. \(B(-1,0)\) (1 point)

Question 6: Describe a similarity transformation (3 points)

Triangle DEF is the image of triangle ABC under a sequence of transformations.

1. Find the scale factor relating \(DE\) to \(AB\). (1 point)
2. Describe a sequence of a dilation and a rigid motion that maps ABC onto DEF. (1 point)
3. Use your sequence to show where C goes. (1 point)

Question 7: AA similarity and a missing side (3 points)

Use the figure.

1. Find \(m\angle C\) and \(m\angle D\). (1 point)
2. Are the triangles similar? Name the criterion and write a similarity statement. (1 point)
3. Find \(EF\). (1 point)

Question 8: Poster dilation (2 points)

Sofia enlarges a 5 inch by 7 inch photo into a poster that is 30 inches wide.

1. Find the scale factor and the height the poster needs for it to be a dilation of the photo. (1 point)
2. The print shop delivers a poster that is 30 inches by 40 inches. Is it a dilation of the photo? Explain. (1 point)

Question 9: Perimeter after a dilation (1 point)

A triangle with sides 5 cm, 12 cm and 13 cm is dilated with scale factor \(\frac{2}{5}\). Find the perimeter of the image.

⬇ Download the Geometry Dilations and Similarity Transformations test (PDF, 93 KB)

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