Graphing Properties

Reflection, Rotation, Symmetry, Translation

2. In the standard (x,y) coordinate plane, point A has coordinates (−7,−5). Point A is translated 7 units to the left and 5 units down, and that image is labeled  A′. What are the coordinates of A ?

Translations

2021 April(D05) Math Question 2

2. A point at (-5,7) in the standard (x,v) coordinate plane is translated right 7 coordinate units and down 5 coordinate units. What are the coordinates of the point after the translation?

2019 June(A11) Math Question 2

2018 December(B05) Math Question 3

2010 December(69A) Math Question 3

2010 April(68G) Math Question 3

2010 June(68C) Math Question 7

10. Triangles nABC and nA′B′C′ are graphed in the standard (x,y) coordinate plane below. Triangle nA′B′C′ is the image of nABC under one of the following transformations. Which one?

Reflection

2020 December(D03) Math Question 10

2012 June(70C) Math Question 11

2019 April(B04) Math Question 15

2019 December(C03) Math Question 16

16. Quadrant I of the standard (x,y) coordinate plane is shown on a large computer screen. A blinking dot is positioned at (2,3). The dot makes exactly 2 moves: first, horizontally in the positive x direction for 4 seconds at a speed of 0.5  coordinate units per second; then, vertically in the positive y direction for 2 seconds at the same speed. At what point is the dot located after these 2 moves?

2021 December(E23) Math Question 16

2011 June(69F) Math Question 22

23. In the standard (x,y) coordinate plane, a translation maps a point (x,y) to its image (x — 5, y + 3). To what image does this translation map (-3,-2) ?

2016 December(74H) Math Question 23

25. The point (6,3) and the line y = 7 are graphed in the standard (x,y) coordinate plane below. After the point has been reflected across the line, what are the coordinates of the point's image?

2015 December(72E) Math Question 25

2009 December(68A) Math Question 29

31. In the standard (x,y) coordinate plane below, ABC
will be translated 10 units down and then the resulting ,
image will be reflected over the y-axis. What will be
the coordinates of the final image of A resulting from
both transformations?

2019 June(B02) Math Question 31

32. The circle will be reflected across the y-axis. What will be the coordinates of the image of the center of the circle?

2015 April(73G) Math Question 32

32. Parallelogram ABCD will be reflected over the y-axis. What will be the coordinates of the image of A ?

2017 June(74C) Math Question 32

2019 December(C03) Math Question 32

32. A series of transformations are applied to the graph in the standard (x,y) coordinate plane below. The graph below is reflected across the x-axis. The new graph is reflected across the y-axis. This new graph is rotated 90° clockwise ( ) about the origin. The resulting graph is one of the following graphs. Which one?

2020 December(D03) Math Question 32

33. In the standard (x,y) coordinate plane, A’ is the image resulting from the reflection of the point A(2,-3) across the y-axis. What are the coordinates of A’ ?

2018 June(A11) Math Question 33

2011 April(67F) Math Question 34

2019 June(72F) Math Question 37

2012 December(71A) Math Question 38

2013 April(71G) Math Question 40

2010 April(68G) Math Question 40

40. Regardless of how the graph is oriented in the standard (x,y) coordinate plane, NO graph in one of the following categories has a vertical line of symmetry. Which one?

Lines of Symmetry

2021 April(Z04) Math Question 40

41. When ABCD is reflected over the y-axis to A'B'C'D', what are the coordinates of D'?

2014 June(72C) Math Question 41

44. Right triangle RST will be rotated about the x-axis to form a right circular cone. How long, in coordinate units, is the radius of the cone's base?

2015 December(72E) Math Question 44

2009 June(67C) Math Question 44

2019 June(72F) Math Question 45

2011 April(67F) Math Question 49

2010 June(68C) Math Question 49

49. A 3rd circle, not shown, is the image resulting from applying the 1st transformation listed below to the smaller circle and then applying the 2nd transformation listed below to the result of the 1st transformation.
1st: A dilation with center O and scale factor 2 2nd: A translation of 8 coordinate units to the
right
The 3rd circle has how many points in common with the larger circle?

2021 June(D06) Math Question 49

52. In the standard (x,y) coordinate plane below, ADEF will be translated 12 coordinate units down and 2 coordinate units right. What will be the coordinates of E after the translation?

2014 April(71H) Math Question 52

53. Point I(3,4) is shown in the standard (x,y) coordinate plane below. Point I is reflected across the line x = 7 and, after the reflection, is labeled J. What are the coordinates of J ?

Reflection, Rotation, Symmetry, TranslationGraphing PropertiesACT math questions

2021 April(D05) Math Question 2

2019 June(A11) Math Question 2