Dilations and Similarity in the Coordinate Plane

Under a dilation, triangle ABC with coordinates

A(–12, –8), B(2, 14), C(6, –6) becomes triangle A’B’C’ with coordinates A’(–18, –12), B’(3, 21), C’(9, –9).

What is the scale factor?

• 6

• 2

• 1.5

• 2.5

Tags

CCSS.8.G.A.3

Which of these series of transformations will result in an image that is NOT congruent to its pre-image? Choose ALL that are correct.

• a reflection over the y-axis followed by a reflection over x-axis

• a translation of 2 along the x-axis followed by a translation of 4 along the y-axis

• a rotation of 90° clockwise about the origin followed by a dilation of factor 2 centered at the origin

• a reflection over the x-axis followed by a dilation of factor 3 centered at the origin and a translation of –4 along the y-axis

• a rotation of 180° counterclockwise about the origin followed by a reflection over the y-axis and a translation of 2 along the x-axis

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Find the scale factor from ABCD to A'B'C'D'. Notice the center of dilation is B.

• 1/2

• 2/5

• 5/2

• 2

Tags

CCSS.8.G.A.3

Suppose a pentagon graphed on a coordinate plane will undergo a dilation. Which of these is a true statement?

• The resulting pentagon will be similar to the original pentagon only if the center of the dilation is the origin.

• The resulting pentagon will be similar to the original pentagon only if the center of the dilation is a vertex ofthe original pentagon.

• The resulting pentagon will be similar to the original pentagon regardless of the center of the dilation.

• The resulting pentagon will not be similar to the original pentagon regardless of the center of the dilation.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

A landscape designer checks the scale model of a square lawn whose coordinates are A(–5, 5), B(–1, 5), C(–1, 1) and D(–5, 1) drafted on a computer program which involves coordinate planes. The scale factor from paper to real life is 10. Which of the following is D'?

• (-.5, -.1)

• (-50, 10)

• (-50, 50)

• (-.5, .5)

Tags

CCSS.7.G.A.1

Miguel claims that if a trapezoid is rotated, reflected, or translated to produce another trapezoid, the two trapezoids are similar. However, he says that if a trapezoid is dilated to produce another trapezoid, the two trapezoids are not similar. Which of these statements are correct? Select threethat apply.

• Miguel is right in saying that if a trapezoid is rotated to produce another trapezoid, the two trapezoids are similar.

• Miguel is right in saying that if a trapezoid is reflected to produce another trapezoid, the two trapezoids are similar.

• Miguel is right in saying that if a trapezoid is translated to produce another trapezoid, the two trapezoids are similar.

• Miguel is right in saying that if a trapezoid is dilated to produce another trapezoid, the two trapezoids are not similar.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Triangle REP has the coordinates

R(1, 5), E(–4, –4) and P(6, –4). If the image, R'E'P', has the coordinate

R'(3, 15), find E' and P'.

• E'(-12, -12) P'(18, -12)

• E'(12, 12) P'(-18, 12)

• E'(0.3, 2.7) P' (2, -1.3)

Tags

CCSS.8.G.A.3

Suppose a triangle with the vertices

(–1, 4), (–1, –2), and (2, –2) were dilated, with the center of dilation at the origin and with a scale factor of 2. Which of these would be a vertex of the dilated figure? Select three that apply.

• (-2, -4)

• (-2, 8)

• (-1, -4)

• (-1, 4)

• (4, -4)

Tags

CCSS.8.G.A.3

• They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/4.

• They are similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

• They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/2.

• They are not similar, because one can be obtained by dilating the other about the origin with a scale factor of 1/4.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

If AD = 7, AB = 21, and DE = 6, find BC.

• 18

• 2

• None of the above.

Tags

CCSS.HSG.CO.C.10