Checkpoint 3 Review and Daily Practice

Find the distance between the points on the coordinate grid.

• 3 Units

• 5 Units

• 7 Units

• 9 Units

Answer explanation

Count the number of units between the two points.

Figure WXYZ 180 degrees clockwise around the origin to form Figure W’X’Y’Z”. What will be the coordinates for W’?

• (-1, 4)

• (1, -4)

• (-4, 5)

• (4, -5)

Answer explanation

Same x and y-values with different signs

Is Figure PQRSTU a translation, rotation, or reflection?

• Translation

• Rotation

• Reflection

Answer explanation

Mirror image across a line of reflection

Translate Triangle XYZ 4 Units right and 2 units down. Where would the coordinates for Z’ be?

• (0, -2)

• (-4, 0)

• (-1, 0)

• (3, -2)

Answer explanation

Figure 1 is a rectangle that has side lengths of 5 in. and 3 in. Figure 1 is dilated by a scale factor of 4 to form Figure 2. Figure 1 is _____ to Figure 2. The area of Figure 2 is _____ times the area of Figure 1. The perimeter of Figure 2 is _____ times the perimeter of Figure 1.

• Congruent, 16, 4

• Similar, 4, 16

• Congruent, 4, 16

• Similar, 16, 4

Answer explanation

The figures are similar because they are the same shape but not the same size.

The area of Figure 2 is 16 times greater than that of Figure 1.

Area of Figure 2-240 square inches

Area of Figure 1-15 square inches

Perimeter of Figure 2-64 inches

Perimeter of Figure 1-16 inches

Which sequence of transformations could be used to obtain Quadrilateral WXYZ from Quadrilateral LMNP?

• Vertical translation, dilation

• 180 degree rotation, dilation

• Dilation, reflection across horizontal line

• Reflection across a horizontal line, vertical translation

Answer explanation

Mirror image across a line moving left to right or right to left

WXYZ is a reduction of LMNP.

Describe a sequence of transformations that maps Trapezoid PQRS onto Trapezoid WXYZ.

• A reflection across the y-axis and a dilation with a scale factor of 1/3

• A reflection across the y-axis and a dilation with a scale factor of 1/2

• A reflection across the y-axis and a translation 3 units up

• A reflection across the x-axis and a dilation with a scale factor of 3

Answer explanation

Rectangle CDEF has vertices C (-10, 10), D (5, 10), E (5, 5), and F (-10, 5). It is dilated by a scale factor of 1/5 centered at (0, 0) to produce Rectangle C’D’E’F’. What are the coordinate of the vertices for Rectangle C’D’E’F’?

• C’ (-2, 2)

  D’ (1, 1)

  E’ (1, 2)

  F’ (-2, 1)

• C’ (-2, 1)

  D’ (1, 1)

  E’ (1, 2)

  F’ (-2, 2)

• C’ (1, 1)

  D’ (1, 2)

  E’ (-1, 2)

  F’ (-2, 1)

• C’ (-2, 2)

  D’ (1, 2)

  E’ (1, 1)

  F’ (-2, 1)

Answer explanation

All coordinates must be divided by 5 or multiplied by 1/5.

Does the pair show a reduction? Why or why not?

• Yes, the shapes are the same and the side lengths are proportional.

• Yes, the shapes are the same and the side lengths are NOT proportional.

• No, the shapes are not the same the side lengths are proportional.

• No, the shapes are the same and the side lengths are not proportional.

Answer explanation

The pair shows a reduction by a scale factor of 1/4.

Triangle ABC has vertices A (2, 4), B (0, -4), and C (-2, -2). It is dilated with a center at (0, 0) to produce A’B’C’ with vertices A’ (5, 10), B’ (0, -10), and C’ (-5, -5). What is the scale factor of the dilation?

• 1.5 or 3/2

• 2

• 2.5 or 5/2

• 3

Answer explanation

You can multiply the original coordinates by 2.5 or 5/2 to achieve the new coordinates. Therefore, the scale factor is 2.5 or 5/2.