Transformational Geometry Test Review

Transformational Geometry Test Review

By B. Cox

​What is a Transformation?

​A transformation is a process which changes the position, and possibly the size and orientation of a shape.

​Translation

​A translation is a transformation that slides

the original figure horizontally and/or vertically.​

​The resulting image is congruent to the original figure.

​Translation

​In this example, the original figure, Triangle ABC was translated 8 units to the left and 4 units down to create Triangle A'B'C'.

Multiple Choice

Which diagram(s) below show a translation of the original figure, to the image?

​Reflection

​A reflection is a transformation that flips

the original figure over a line of reflection.

​The resulting image is congruent to the original figure.

​Reflection

​In this example, the original figure, triangle ABC was reflection in the x-axis.

The points in the original figure and the points in the image are equal distances away from the x-axis. ​

​Reflection

​In this example, the original figure, triangle ABC was reflection in the y-axis.

The points in the original figure and the points in the image are equal distances away from the y-axis. ​

Multiple Select

Which diagram(s) below show a reflection of the original figure, to the image? Check all that apply.

​Rotation

​A rotation is a transformation that turns

the original figure a given number of degrees around a center of rotation.

The resulting image is congruent to the original figure.

​Rotation

​When the angle of rotation is positive, the figure turns counterclockwise.

​Rotation

​In this example, triangle ABC has been rotated 90 degrees to produce triangle A'B'C'.

​​The rule for a 90 degree rotation is:

​(x,y)→(-y,x)

​Rotation

​In this example, triangle ABC has been rotated 180 degrees to produce triangle A'B'C'.

​​The rule for a 180 degree rotation is:

​(x,y)→(-x,-y)

​Rotation

​In this example, triangle ABC has been rotated 270 degrees to produce triangle A'B'C'.

​​The rule for a 270 degree rotation is:

​(x,y)→(y,-x)

Multiple Select

Which diagram(s) below show a rotation of the original figure, to produce the image? Check all that apply.

Multiple Choice

If triangle ABC is rotated 90 degrees to produce its image, which quadrant will the image end up in?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

If triangle ABC is rotated 90 degrees to produce its image, what will be the coordinates of A'?

• $$\left(1,-2\right)$$  

• $$\left(1,2\right)$$  

• $$\left(2,1\right)$$  

• $$\left(-2,-1\right)$$  

Multiple Choice

If triangle ABC is rotated 180 degrees to produce its image, which quadrant will the image end up in?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

If triangle ABC is rotated 180 degrees to produce its image, what will be the coordinates of B'?

• $$\left(-4,2\right)$$  

• $$\left(-2,4\right)$$  

• $$\left(2,4\right)$$  

• $$\left(-4,-2\right)$$  

Multiple Choice

If triangle ABC is rotated 270 degrees to produce its image, which quadrant will the image end up in?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

If triangle ABC is rotated 270 degrees to produce its image, what will be the coordinates of C'?

• $$\left(-4,3\right)$$  

• $$\left(-4,-3\right)$$  

• $$\left(-3,-4\right)$$  

• $$\left(4,3\right)$$  

​Dilation

​A dilation is a transformation that enlarges or shrinks

the original figure a given scale factor around a center of dilation.

The resulting image is similar to the original figure.

​Scale Factor

​The scale factor of a dilation is the number that is multiplied by the original coordinates to produce the image.

A Scale Factor greater than 1 will enlarge the image.

A Scale Factor less than 1 will shrink the image. ​

​Scale Factor

​The diagram shows a dilation with a scale factor of 2.

Multiple Choice

What is the scale factor of the dilation shown in the diagram?

• $$6$$  

• $$-6$$  

• $$3$$  

• $$\frac{1}{3}$$  

Multiple Choice

What is the scale factor of the dilation shown in the diagram?

• $$-6$$  

• $$-9$$  

• $$4$$  

• $$\frac{1}{4}$$  

Multiple Choice

If triangle ABC is dilated by a scale factor of 2 to produce its image, what will be the coordinates of A'?

• $$\left(3,3\right)$$  

• $$\left(7,7\right)$$  

• $$\left(\frac{5}{2},\frac{5}{2}\right)$$  

• $$\left(10,10\right)$$  

Multiple Choice

If triangle ABC is dilated by a scale factor of $$\frac{1}{2}$$   to produce its image, what will be the coordinates of C'?

• $$\left(6,2\right)$$  

• $$\left(24,8\right)$$  

• $$\left(4,2\right)$$  

• $$\left(3,2\right)$$