Transformations, Similarity, and Congruence

An architect is creating a scale drawing of a garden, which is similar to the actual garden. A right triangular grassland, in the garden, has a base of 12 inches and a height of 7.5 inches in the architect's drawing. If the actual base of the grassland is 36 feet, what is the actual height of the grassland?

• 18.75 feet

• 3 feet

• 2.5 feet

• 22.5 feet

Tags

CCSS.7.G.A.1

Which transformation describes the change in the letter R?

• translation

• reflection

• rotation

• cannot be determined

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Which transformation results in a figure that is similar to the original figure but has a greater area?

• A dilation of triangle QRS by a scale factor of 0.25

• A dilation of triangle QRS by a scale factor of 0.5

• A dilation of triangle QRS by a scale factor of 1

• A dilation of triangle QRS by a scale factor of 2

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

In the coordinate plane, segment PQ is the result of a dilation of segment XY by a scale factor of 1/2. Which point is the center of dilation?

• (-4, 0)

• (0, -4)

• (0, 4)

• (4, 0)

Tags

CCSS.8.G.A.3

The smaller triangle is transformed to create the larger triangle. Which of these is the scale factor of the dilation center at the origin?

• 4

• 2

• 1

• 1/2

Tags

CCSS.HSG.CO.A.2

Look at quadrilateral QRST. What is the image of point R after a counterclockwise rotation of 270 degrees about the origin?

• (6, -3)

• (-3, 6)

• (-6, 3)

• (3, -6)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

In the triangles shown, ∆ABC is dilated by a factor of 2/3 to form ∆XYZ. Given that m<A=50° and m<B=100°, what is m<Z?

• 15 degrees

• 25 degrees

• 30 degrees

• 50 degrees

Tags

CCSS.8.G.A.3

• 2.0

• 4.5

• 7.5

• 8.0

Tags

CCSS.HSG.SRT.B.4

Parallelogram FGHJ was translated 3 units down to form parallelogram F’G’H’J’. Parallelogram F’G’H’J’ was then rotated 90° counterclockwise about point G’ to obtain F’’G’’H’’J’’. Which statement is true about parallelogram FGHJ and parallelogram F”G”H”J”?

• The figures are both similar and congruent.

• The figures are neither similar nor congruent.

• The figures are similar but not congruent.

• The figures are congruent but not similar.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

In this diagram, DE is congruent to JI and angle D is congruent to angle J. Which additional information is sufficient to prove that ∆DEF is congruent to ∆JIH?

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Tags

CCSS.HSG.SRT.B.5