G.SRT.A.1.LineDilations.doc



1 On the set of axes below, [pic] is dilated by a scale factor of [pic] centered at point P.

[pic]

Which statement is always true?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

2 A line segment is dilated by a scale factor of 2 centered at a point not on the line segment. Which statement regarding the relationship between the given line segment and its image is true?

1) The line segments are perpendicular, and the image is one-half of the length of the given line segment. 2) The line segments are perpendicular, and the image is twice the length of the given line segment. 3) The line segments are parallel, and the image is twice the length of the given line segment. 4) The line segments are parallel, and the image is one-half of the length of the given line segment.

3 The line whose equation is [pic] is dilated by a scale factor of [pic] centered at the origin. Which statement is correct?

1) The image of the line has the same slope as the pre-image but a different y-intercept. 2) The image of the line has the same y-intercept as the pre-image but a different slope. 3) The image of the line has the same slope and the same y-intercept as the pre-image. 4) The image of the line has a different slope and a different y-intercept from the pre-image.

4 If the line represented by [pic] is dilated by a scale factor of 4 centered at the origin, which statement about the image is true?

1) The slope is [pic] and the y-intercept is [pic]. 2) The slope is [pic] and the y-intercept is [pic]. 3) The slope is [pic] and the y-intercept is [pic]. 4) The slope is [pic] and the y-intercept is [pic].

5 A line that passes through the points whose coordinates are [pic] and [pic] is dilated by a scale factor of 3 and centered at the origin. The image of the line

1) is perpendicular to the original line 2) is parallel to the original line 3) passes through the origin 4) is the original line

6 A line is dilated by a scale factor of [pic] centered at a point on the line. Which statement is correct about the image of the line?

1) Its slope is changed by a scale factor of [pic]. 2) Its y-intercept is changed by a scale factor of [pic]. 3) Its slope and y-intercept are changed by a scale factor of [pic]. 4) The image of the line and the pre-image are the same line.

7 An equation of line p is [pic]. An equation of line q is [pic]. Which statement about lines p and q is true?

1) A dilation of [pic] centered at the origin will map line q onto line p. 2) A dilation of 2 centered at the origin will map line p onto line q. 3) Line q is not the image of line p after a dilation because the lines are not parallel. 4) Line q is not the image of line p after a dilation because the lines do not pass through the origin.

8 A three-inch line segment is dilated by a scale factor of 6 and centered at its midpoint. What is the length of its image?

1) 9 inches 2) 2 inches 3) 15 inches 4) 18 inches

9 Line segment [pic], whose endpoints are [pic] and [pic], is the image of [pic] after a dilation of [pic] centered at the origin. What is the length of [pic]?

1) 5 2) 10 3) 20 4) 40

10 In the diagram below, [pic] is the image of [pic] after a dilation of scale factor k with center E.

[pic]

Which ratio is equal to the scale factor k of the dilation?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

11 After a dilation centered at the origin, the image of [pic] is [pic]. If the coordinates of the endpoints of these segments are [pic], [pic], [pic], and [pic], the scale factor of the dilation is

1) [pic] 2) [pic] 3) 3 4) [pic]

12 After a dilation with center [pic], the image of [pic] is [pic]. If [pic] and [pic], the scale factor of this dilation is

1) [pic] 2) 5 3) [pic] 4) 4

13 The line represented by [pic] is dilated by a scale factor of k centered at the origin, such that the image of the line has an equation of [pic]. What is the scale factor?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

14 On the graph below, point [pic] and [pic] with coordinates [pic] and [pic] are graphed.

[pic]

What are the coordinates of B’ and C’ after [pic] undergoes a dilation centered at point A with a scale factor of 2?

1) [pic] and [pic] 2) [pic] and [pic] 3) [pic] and [pic] 4) [pic] and [pic]

15 On the set of axes below, the endpoints of [pic] have coordinates [pic] and [pic].

[pic]

If [pic] is dilated by a scale factor of 2 centered at [pic], what are the coordinates of the endpoints of its image, [pic]?

1) [pic] and [pic] 2) [pic] and [pic] 3) [pic] and [pic] 4) [pic] and [pic]

16 The line [pic] is transformed by a dilation centered at the origin. Which linear equation could represent its image?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

17 The line [pic] is transformed by a dilation centered at the origin. Which linear equation could be its image?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

18 The line represented by the equation [pic] is transformed by a dilation centered at the origin. Which linear equation could represent its image?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

19 The equation of line h is [pic]. Line m is the image of line h after a dilation of scale factor 4 with respect to the origin. What is the equation of the line m?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

20 The equation of line t is [pic]. Line m is the image of line t after a dilation with a scale factor of [pic] centered at the origin. What is an equation of the line m?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

21 The line [pic] is dilated by a scale factor of [pic] and centered at the origin. Which equation represents the image of the line after the dilation?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

22 What is an equation of the image of the line [pic] after a dilation of a scale factor of [pic] centered at the origin?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

23 Line [pic] is transformed by a dilation with a scale factor of 2 and centered at [pic]. The line's image is

1) [pic] 2) [pic] 3) [pic] 4) [pic]

24 Line MN is dilated by a scale factor of 2 centered at the point [pic]. If [pic] is represented by [pic], which equation can represent [pic], the image of [pic]?

1) [pic] 2) [pic] 3) [pic] 4) [pic]

25 Line [pic] is mapped onto line m by a dilation centered at the origin with a scale factor of 2. The equation of line [pic] is [pic]. Determine and state an equation for line m.

26 The coordinates of the endpoints of [pic] are [pic] and [pic]. Determine the length of [pic], the image of [pic], after a dilation of [pic] centered at the origin. [The use of the set of axes below is optional.]

[pic]

27 Aliyah says that when the line [pic] is dilated by a scale factor of 2 centered at the point [pic], the equation of the dilated line is [pic]. Is Aliyah correct? Explain why. [The use of the set of axes below is optional.]

[pic]

28 Line n is represented by the equation [pic]. Determine and state the equation of line p, the image of line n, after a dilation of scale factor [pic] centered at the point [pic]. [The use of the set of axes below is optional.] Explain your answer.

[pic]

1 ANS: 2 REF: 081901geo

2 ANS: 3 REF: 061706geo

3 ANS: 1 REF: 011814geo

4 ANS: 1

A dilation by a scale factor of 4 centered at the origin preserves parallelism and [pic].

REF: 081910geo

5 ANS: 2 REF: 011610geo

6 ANS: 4 REF: 062223geo

7 ANS: 3 REF: 082212geo

8 ANS: 4

[pic]

REF: 061602geo

9 ANS: 4

[pic]

REF: 081621geo

10 ANS: 1 REF: 061518geo

11 ANS: 1

[pic]

REF: 061905geo

12 ANS: 4

[pic]

REF: 011901geo

13 ANS: 1

[pic] [pic]

REF: 012008geo

14 ANS: 1

[pic]

REF: 011713geo

15 ANS: 4

[pic]

REF: 012322geo

16 ANS: 2

The slope of [pic] is [pic].

REF: 061907geo

17 ANS: 1

The line [pic] does not pass through the center of dilation, so the dilated line will be distinct from [pic]. Since a dilation preserves parallelism, the line [pic] and its image [pic] are parallel, with slopes of [pic].

REF: 061522geo

18 ANS: 1

Since a dilation preserves parallelism, the line [pic] and its image [pic] are parallel, with slopes of [pic].

REF: 081710geo

19 ANS: 2

The given line h, [pic], does not pass through the center of dilation, the origin, because the y-intercept is at [pic]. The slope of the dilated line, m, will remain the same as the slope of line h, -[pic]. All points on line h, such as [pic], the y-intercept, are dilated by a scale factor of 4; therefore, the y-intercept of the dilated line is [pic] because the center of dilation is the origin, resulting in the dilated line represented by the equation [pic].

REF: spr1403geo

20 ANS: 4

Another equation of line t is [pic]. [pic]

REF: 012319geo

21 ANS: 2

The line [pic] does not pass through the center of dilation, so the dilated line will be distinct from [pic]. Since a dilation preserves parallelism, the line [pic] and its image will be parallel, with slopes of 2. To obtain the y-intercept of the dilated line, the scale factor of the dilation, [pic], can be applied to the y-intercept, [pic]. Therefore, [pic]. So the equation of the dilated line is [pic].

REF: fall1403geo

22 ANS: 4

The line [pic] does not pass through the center of dilation, so the dilated line will be distinct from [pic]. Since a dilation preserves parallelism, the line [pic] and its image will be parallel, with slopes of [pic]. To obtain the y-intercept of the dilated line, the scale factor of the dilation, [pic], can be applied to the y-intercept, [pic]. Therefore, [pic]. So the equation of the dilated line is [pic].

REF: 011924geo

23 ANS: 4

The line [pic] passes through the center of dilation, so the dilated line is not distinct.

REF: 081524geo

24 ANS: 2

The line [pic] passes through the center of dilation, so the dilated line is not distinct.

REF: 061824geo

25 ANS:

[pic]

REF: 011631geo

26 ANS:

[pic] [pic]

REF: 081729geo

27 ANS:

No, The line [pic] passes through the center of dilation, so the dilated line is not distinct. [pic]

REF: 081830geo

28 ANS:

[pic] The line is on the center of dilation, so the line does not change. [pic]

REF: 061731geo

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