Regents Transformation Questions Answers

Regents Prep Transformation Questions Answers Review Sheet.

1) The three vertices of triangle ABC lie in Quadrant I.  If triangle ABC is reflected in the x-axis, what Quadrant will its image lie in?

2) Find the image of (3,5) after a reflection in the line y = x.

3) When point (-2,5) is reflected  in the line x = 1, what are the coordinates of the new image?

4)  When point (-4,-7) is reflected  in the line y = -2, what are the coordinates of the new image?

5) If a translation maps (2,3) onto (4,8).  What are the coordinates  of B′, the image of B(4,6) under the same translation?

6) Under what type of transformation can the image be a different size than the original figure?

7) Under e dilation with a constant of k, the image of point (2,3) is (8,12).  What is the value of k?

8) Which of the following letters has both point and line symmetry?

  • a) A
  • B) X
  • C) M
  • D) T

9) What is the total number of lines of symmetry for letter “A”?

10) Triangle ABC has coordinates A(3,4), B(1,7), and C(3,7). 

  • A) Draw and label ABC.
  • B) Graph and state the coordinates of A′B′C′, the image of ABC after a reflection in the x-axis.
  • C) Graph and state the coordinates of A′′B′′C′′, the image of A′B′C′ after a reflection in the line y = x.
  • D) Graph and state the coordinates of A′′′B′′′C′′′, the image of A′′B′′C′′ after a translation of (x +5, y -1).

11) Triangle ABC has coordinates A(1,0), B(7,4), and C(5,7).

  • A) Draw and label ABC.
  • B) Graph and state the coordinates of A′B′C′, the image of ABC after a reflection in the origin.
  • C) Graph and state the coordinates of A′′B′′C′′, the image of ABC after a dilation of 2.
  • D) Graph and state the coordinates of A′′′B′′′C′′′, the image of ABC after a rotation of 270°.

12) The image of triangle DEF under a point of reflection is triangle D′E′F′.  Find the coordinates of the point of reflection when: D(-3,6), E(5,5), F(2,4) and D′(-1,0), E′-5,1), and F′(-6,2).

13) The coordinates of ΔGLD are G(1,-5), L(6,-4), and D(3,-1).

  1. Draw and label ΔGLD.
  2. Draw and label ΔG’L’D’, the image of ΔGLD after T-8,0.
  3. Draw and label ΔG’’L’’D’’, the image of ΔG’L’D’ after rx-axis.
  4. What single transformation maps ΔGLD onto ΔG’’L’’D’’?
  5. Draw and label ΔG’’’L’’’D’’’, the image of ΔGLD after T-8,0 ◦ rx-axis. How does this image compare to ΔG’’L’’D’’?

14) The coordinates of ΔABC are A(3,2), B(7,6), and C(7,1).

  • A) On the coordinate plane, draw and label ΔABC.
  • B) Graph and state the coordinates of ΔA’B’C’, the image of ΔABC after rx-axis.
  • C) Graph and state the coordinates of ΔA’’B’’C’’, the image of ΔA’B’C’ after T0,-7.
  • D) Which of the above transformations is an example of a direct isometry?

15) Graph each of the following lines:

  • A) y = -9x + 8
  • B) 2x – 3y = 9
  • C) x = 7
  • D) y = -3

16) Find the equation in slope-intercept form:

  • a) (-4,1)(-8,6)
  • b) (3,-2)(-6,-8)
  • c) (-9,8)(-9,6)

17) Find the equation in slope-intercept form:

  • A) m = 2; (-1,8)
  • B) m = 2/3; (-6,-7)
  • C) m = 0; (-7,4)

18) Graph the following equations:

  • A) (x + 2)2 + y2 = 49
  • B) (x – 3)2 + (y +8)2 = 4

19) Find the equation in slope-intercept form:

  • a) For the line parallel to the line y – 2x = 8 that passes through the point (-3,4).
  • b) For the line perpendicular to y = 4 and passes through the point (-1,5).
  • c) For the line perpendicular to y = 1/2x – 6 that passes through the point (-4,5).

Transformation Review Sheet Answer Key:

1) Quadrant IV

2) (5, 3)

3) (4, 5)

4) (-4, 3)

5) (6, 11)

6) Dilation

7) k = 4

8) b) X

9) one

10)       b) A'(3, -4)                  B'(1, -7)           C'(3, -7)

  1. c) A”(-4, 3) B”(-7, 1)          C”(-7, 3)
  2. d) A”'(1, 2) B”'(-2, 0)         C”'(-2, 2)

11)       b) A'(-1, 0)                  B'(-7, -4)          C'(-5, -7)

  1. c) A”(2, 0) B”(14, 8)         C”(-10, 14)
  2. d) A”'(0, -1) B”'(4, -7)         C”'(7, -5)

12) Change coordinate E’ to (-5, -1)

Point of Reflection is (-2, 3)

13)       b) G`(-7,-5)                  L`(-2,-4)          D`(-5,-1)

  1. c) G“(-7,5) L“(-2,4)          D“(-5,1)
  2. d) Glide Reflection
  3. e) same image

14)       b) A`(3,-2)                   B`(7,-6)           C`(7,-1)

  • c) A“(3,-9) B“(7,-13)        C“(7,-8)
  • d) Translation

15)       a) m = -9         y-int = 8

  • b) m = 2/3 y-int = -3
  • c) Vertical Line
  • d) Horizontal Line

16)       a) y = -4/5x + 4.2        b) y = 3/2x – 6.5         c) x = -9

17)       a) y = 2x + 10              b) y = 2/3x + 3            c) y = 4

18)       a) Center = (-2,0)        Radius = 7                   b) Center = (3,-8)        Radius = 2

19)       a) y = 2x – 2                b) x = -1                      c) y = -2x – 3

See also: 

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