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1. Transformations
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United States of AmericaNC
Math 2

1.04 Dilations

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Practice

Interactive practice questions

Identify if rectangle $A'B'C'D'$A′B′C′D′ is a dilation of rectangle $ABCD$ABCD.

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A coordinate plane is marked from 0 to 20 on both $x$x- and $y$y- axes with two quadrilaterals drawn. Quadrilateral ABCD is smaller and is formed with vertices A $\left(3,4\right)$(3,4), B $\left(8,4\right)$(8,4), C $\left(8,9\right)$(8,9), and D $\left(3,9\right)$(3,9). quadrilateral A'B'C'D' is larger and is formed with vertices A' $\left(6,8\right)$(6,8), B' $\left(15,8\right)$(15,8), C' $\left(15,18\right)$(15,18), and D' $\left(6,18\right)$(6,18). Please dont provide the distance formula as hint.

no

A

yes

B
Easy
< 1min

Identify if triangle $A'B'C'$A′B′C′ is a dilation of triangle $ABC$ABC.

Easy
< 1min

Identify if triangle $A'B'C'$A′B′C′ is a dilation of triangle $ABC$ABC.

Easy
< 1min

Identify if quadrilateral $A'B'C'D'$A′B′C′D′ is a dilation of quadrilateral $ABCD$ABCD.

Easy
< 1min
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Outcomes

NC.M2.F-IF.1

Extend the concept of a function to include geometric transformations in the plane by recognizing that: • the domain and range of a transformation function f are sets of points in the plane; • the image of a transformation is a function of its pre-image.

NC.M2.F-IF.2

Extend the use of function notation to express the image of a geometric figure in the plane resulting from a translation, rotation by multiples of 90 degrees about the origin, reflection across an axis, or dilation as a function of its pre-image.

NC.M2.G-CO.2

Experiment with transformations in the plane. • Represent transformations in the plane. • Compare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both distance and angle measure (e.G. Stretches, dilations). • Understand that rigid motions produce congruent figures while dilations produce similar figures.

NC.M2.G-SRT.1

Verify experimentally the properties of dilations with given center and scale factor:

NC.M2.G-SRT.1a

When a line segment passes through the center of dilation, the line segment and its image lie on the same line. When a line segment does not pass through the center of dilation, the line segment and its image are parallel.

NC.M2.G-SRT.1b

The length of the image of a line segment is equal to the length of the line segment multiplied by the scale factor.

NC.M2.G-SRT.1c

The distance between the center of a dilation and any point on the image is equal to the scale factor multiplied by the distance between the dilation center and the corresponding point on the pre-image.

NC.M2.G-SRT.1d

Dilations preserve angle measure.

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