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Two-Dimensional Shapes

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Analyze transformations on the coordinate plane and explain their effects on figures.

Questions

Skill type

two dimensional-shapes

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Practice + review

Sample questions

Question

A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated using the origin as the center of dilation. Which rule could represent this dilation?

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Question

Triangle TRW is shown on the coordinate grid. y 6 T 5 4 3 2 1 −6 6−5 −4 −3 −2 −11 2 3 4 5x −1 −2 −3 −4 −5 R −6 W Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle TR′′W ′. Which ordered pair best represents the location of point R′ ?

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Question

A transformation is applied to a figure to create a new figure on a coordinate grid. Which transformation does NOT preserve congruence?

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Question

Polygon LMNPQR is shown on the coordinate grid and models the shape of a garden in a park. Polygon LMNPQR will be dilated with the origin as the center of dilation to create polygon LM′′N′P′ Q′R′ . The vertex Q′ will be located at (21, 7). y 15 14 M 13 12 L N 11 10 9 8 Garden 7 6 5 4 R P 3 2 Q 1 0 1234567891011 x Which rule best represents the dilation?

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Question

$A rectangle is graphed on a coordinate grid. Which transformation will result in a rectangle that is NOT congruent to the original rectangle?$ Open full-size question

A.
$Answer A: A dilation by a scale factor of 3$
B.
$Answer B: A rotation of 180° counterclockwise$
C.
$Answer C: A translation 90 units to the right$
D.
$Answer D: A reflection across the x-axis$

Question

$A circle is graphed on a coordinate grid with its center at (− 4, 7). The circle will be translated p units to the right and v units down. Which rule describes the center of the new circle after this translation?$ Open full-size question

A.
$Answer A: (x, y ) → (− 4 +p, 7 +v)$
B.
$Answer B: (x, y ) → (− 4 +p, 7 −v)$
C.
$Answer C: (x, y ) → (− 4 −p, 7 −v)$
D.
$Answer D: (x, y ) → (− 4 −p, 7 +v)$

Question

$The table shows the coordinates of the vertices of pentagon ABCDE. x y − 1 1 1 6 4 1 2 − 5 − 6 − 2 Pentagon ABCDE is dilated by a scale factor of 7_ 3 with the origin as the center of dilation to create pentagon A′B ′C′D′E′. If (x, y) represents the location of any point on pentagon ABCDE, which ordered pair represents the location of the corresponding point on pentagon A′B ′C′D′E′?$ Open full-size question

A.
$Answer A: ( _3, _3) 7 x 7 y$
B.
$Answer B: (x + 7_ _ 7 ) 3 , y + 3$
C.
$Answer C: (x + 3_ _ 3 ) 7 , y + 7$
D.
$Answer D: ( _7 x, _7 y) 3 3$

Question

$Quadrilateral PQRS is dilated with the origin as the center of dilation to create quadrilateral P′Q′R′S′. The coordinates of each vertex are integers. y P 12 11 10 9 8 7 6 5 4 Q S 2 3 1 −1 −12 −11 0 −9 −8 −7 −6 −5 −4 −3 −2 −1−1 12 34 5 6 x −2 −3 −4 −5 −6 R Which statement is true?$ Open full-size question

A.
$Answer A: Each side length of quadrilateral PQRS is 2_1 the corresponding side length of quadrilateral P′Q′R′S′.$
B.
$Answer B: Quadrilateral P′Q′R′S′ is congruent to quadrilateral PQRS.$
C.
$Answer C: Each angle measure of quadrilateral PQRS is 1_ 2 the corresponding angle measure of quadrilateral P′Q′R′S′.$
D.
$Answer D: Quadrilateral P′Q′R′S′ is similar to quadrilateral PQRS.$

Question

$The coordinates of the vertices of triangle XYZ are X( −2, −1), Y(6, 8) and Z(8, 4). Triangle XYZ is dilated by a scale factor of 3_ 2 with the origin as the center of dilation to create triangle X′Y′Z′. y 9 8 7 6 5 4 3 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 x −1 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 −9 If (x, y ) represents the location of any point on triangle XYZ, which ordered pair represents the location of the corresponding point on triangle X′Y′Z′?$ Open full-size question

A.
$Answer A: ( _3, _3 y) 2 x 2$
B.
$Answer B: (x + 2_ _ 3 , y + 3 ) 2$
C.
$Answer C: ( _2, _2) 3 x 3 y$
D.
$Answer D: (x + 2_ _ 2 ) 3 , y + 3$

Question

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Question

A square is shown on the coordinate grid.

Which transformation does NOT produce a square with vertices at the same set of coordinate pairs?

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Question

Polygon A has an area of 27r square meters. Polygon A is dilated by a scale factor of 3 to create Polygon B.

What is the area in square meters of Polygon B?

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Question

Square ABCD is translated 3 units to the right on a coordinate grid to create square Which rule describes this translation?

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Question

Triangle RST is rotated counterclockwise about the origin of a coordinate plane to create triangle Which rule describes this transformation?

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Question

Quadrilateral is transformed, creating quadrilateral

Which rule describes the transformation applied to quadrilateral to create quadrilateral

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Question

Quadrilateral JKLM is transformed to form quadrilateral J’K’L’M’. Which transformation does NOT preserve congruence?

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Question

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Question

$Triangle JKL is dilated with the origin as the center of dilation to create triangle JK′′L′. y 9 J′ 8 7 K′ 6 5 J 4 K 3 2 1 −4 −3 −2 −1 −1 2 3 4 5 6 7 8 9 10 11 12 13 14x 1 −2 −3 −4 −5 L −6 −7 −8 L′ −9 Which rule best represents the dilation that has been applied to triangle JKL to create triangle JK′′L′?$ Open full-size question

A.
$Answer A: (xy, ) → (x + 6, y −− 3)$
B.
$Answer B: (xy, ) → (x + 4.5, y + 3)$
C.
$Answer C: (, )xy) → ( x,1 1 y 2 2$
D.
$Answer D: (, )xy) → ( x,7 7 y 4 4$

Question

$A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation. If (,xy) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?$ Open full-size question

A.
$Answer A: (20 x, 20 y )$
B.
$Answer B: (0.4 x, 0.4 y )$
C.
$Answer C: (x + 20, y + 20)$
D.
$Answer D: (x + 0.4, y + 0.4)$