Transformations Geometry

A transformation in which a graph or geometric figure is picked up and moved to another  location without any change in size or direction.

• Translation

• Rotation

• Reflection

• Dilation

The vertices of ΔJKL are J(-2, 8), K(1, -3), and L(5, 4). If ΔJKL is transformed following the rule (x, y)→(x+6, y-1), what are the coordinates of the vertices of ΔJ′K′L′?

• (7, -4)

• J'

• (11, 3)

• K'

• (4, 7)

• L'

Match each point with the coordinates of its image after the following sequence of transformations:​

-First transformation: Rotate 90° clockwise about the origin.

-Second transformation: Translate (x, y)→(x + 1, y - 2).

A'​ ​ (a)   B' ​ ​ (b)   C' ​ (c)   D' ​ (d)  

• (1, 7)

• (7, 1)

• (5, -2)

• (3, 0)

• (-1, 7)

• (-5, -2)

• (3, -8)

On the set of axes below, ΔLET and ΔL"E"T" are graphed in the coordinate plane where ΔLET≅ΔL"E"T". Which sequence of rigid motions maps ΔLET onto ΔL"E"T"?

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

• A rotation of 90° counterclockwise about the origin followed by a reflection over the y-axis.

• A rotation of 180° about the origin.

• A reflection over the x-axis followed by a rotation of 90° clockwise about the origin

Triangle BAT has vertices B(2, 1), A(6, 2), and T(3, 6). If ΔBAT is transformed by a rotation of 270° counterclockwise about the origin followed by a translation with rule (x, y)→(x+3,y+6), what will be the coordinates of the final image of point A after the two transformations?

A' ​ (a)  

• ( 5, 0)

• -6, 3)

• (6, -3)

• (2, -6)

• (9, 3)

Given △ABC determine the coordinates of △A’B’C’ after a translation up 1 unit and left 2 units, followed by a dilation with center at the origin and scale factor 0.5.

• A′(-2, 1), B′(0, -2), and C′(1, 2)

• A′(-2, 2), B′(0, -4), and C′(1, 4)

• A′(-4, 2), B′(0, 6), and C′(2, 4)

• A′(-8, 4), B′(0, 12), and C′(4, -8)

Triangle ABC and triangle ADE are shown. Select all the transformations that could be performed to carry triangle ABC onto triangle ADE.

• A reflection across the line y=-x

• A reflection across the x-axis, and then a reflection across the y-axis

• A rotation of 90 degrees clockwise about the origin,  and then a reflection across the x-axis

• A rotation of 90 degrees clockwise about the origin, and then a reflection across the y-axis

Given: ∆AEC, ∆DEF, and \overline{FE\ } \perp\ \overline{CE} What is a correct sequence of similarity transformations that shows ∆AEC~∆DEF?

• A rotation of 180 degrees about point E followed by a horizontal translation

• A rotation of 180 degrees about point E followed by a dilation with a scale factor of 2 centered at point E

• A counterclockwise rotation of 90 degrees about point E followed by a dilation with a scale factor of 2 centered at point E

• A counterclockwise rotation of 90 degrees about point E followed by a horizontal translation

Segment FG with endpoints F(0, -3) and G(0, -1) is translated 2 units up and 3 units to the left. What is the rule for this transformation?​ ​ (a)  

What are the coordinates of F’ and G’.​ ​ (b)  

• (x - 3), (y + 2)

• F' (-3, -1) G' (-3, 1)

• (x - 2), (y + 3)

• (x - 2, y + 3)

• F' (2, 0), G' (2, -4)

Segment FG with endpoints F(0, -3) and G(0, -1) is reflected over the x-axis.

What is the rule for this transformation? ​​ (a)  

What are the coordinates of F’ and G’?

F' ​ (b)   G' ​ (c)  

• (0, 3)

• (0, 1)