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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

Study mode

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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Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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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Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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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Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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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Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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

F.
$Answer F: A dilation by a scale factor of 3$
G.
$Answer G: A rotation of 180° counterclockwise$
H.
$Answer H: A translation 90 units to the right$
J.
$Answer J: A reflection across the x-axis$

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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

F.
$Answer F: (x, y ) → (− 4 +p, 7 +v)$
G.
$Answer G: (x, y ) → (− 4 +p, 7 −v)$
H.
$Answer H: (x, y ) → (− 4 −p, 7 −v)$
J.
$Answer J: (x, y ) → (− 4 −p, 7 +v)$

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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

F.
$Answer F: ( _3, _3) 7 x 7 y$
G.
$Answer G: (x + 7_ _ 7 ) 3 , y + 3$
H.
$Answer H: (x + 3_ _ 3 ) 7 , y + 7$
J.
$Answer J: ( _7 x, _7 y) 3 3$

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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.
$Answer D: Quadrilateral P′Q′R′S′ is similar to quadrilateral PQRS.$

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

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.
$Answer D: (x + 2_ _ 2 ) 3 , y + 3$