Tenth Grade (Grade 10) Symmetry and Transformations Questions for Tests and Worksheets

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Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

The coordinates of the vertices of

$Delta ABC$ are A(3,2), B(4,5), and C(1,1). The coordinates of the vertices of

$Delta LMN$ are L(8,-2), M(10,4), and N(4,-4). Which of the following sequences of transformations, applied to

$Delta ABC$ , shows that

$Delta ABC \ ~ \ Delta LMN ?$

A translation of 2 units right and 2 units down, and then a dilation of factor $3/2$ centered at the origin.
A translation of 2 units right, a reflection over the x-axis, and then a dilation of factor 3 centered at the origin.
A translation of 1 unit right and 3 units down, and then a dilation of factor 2 centered at the origin.
A translation of 3 units left and 1 unit up, and then a dilation of factor -2 centered at the origin.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

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Which of the following sequences of transformations would map

$bar{AB}$ onto

$bar{LM}$ , such that point A corresponds with point L and point B with point M?

Reflection over the y-axis, translation of one unit right, reflection over the x-axis.
Reflection over the x-axis, translation 7 units right.
Rotation of 90° about the origin, translation 3 units down.
Reflection over the line y = x, translation 7 units right, translation 4 units down.

Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8

You are given two triangles, ABC and GHF, plotted on a set of axes. You know that you can map

$bar{AB}$ onto

$bar{GH}$ by a reflection over the x-axis and a rotation of 160° clockwise about the origin. You also know that

$ang A ~= ang G$ and

$ang B ~= ang H$ . Which of the following statements are true? There may be more than one correct answer.

$Delta ABC ~= Delta GHF$
$bar{BC}$ can be mapped onto $bar{HF}$ by a reflection over the x-axis and a rotation of 160° clockwise about the origin.
$bar{AC}$ can be mapped onto $bar{GF}$ by a reflection over the x-axis and a rotation of 160° clockwise about the origin.
$m ang C = m ang F + 160°$

Grade 10 Symmetry and Transformations

In a plane, two congruent figures can be mapped onto one another by a composition of at most reflections.

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Which of the following correctly states the relationship between the side lengths of the pre-image

$Delta ABC$ and the side lengths of the image

$Delta A'B'C' ?$

$(A'B')/(AB) = (B'C')/(BC) = (A'C')/(AC)$
$A'B' = 2AB, \ B'C' = 2BC, \ A'C' = 2AC$
$A'B' + B'C' + A'B' = 1/3(AB+ BC+ AC)$
$A'B'^2 = BC^2 + AC^2, \ B'C'^2 = AB^2 +AC^2, \ A'C'^2 = AB^2 + BC^2$

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Which of the following correctly states the relationship between the angle measures of the pre-image

$Delta ABC$ and the angle measures of the image,

$Delta A'B'C' ?$

$m ang B'A'C' = m ang BAC^2 , \ m ang A'B'C' = m ang ABC ^2, \ m ang A'C'B' = m ang ACB ^2$
$m ang BAC = 2m ang B'A'C', \ m ang ABC = 2m ang A'B'C', \ m ang ACB = 2m ang A'C'B'$
$m ang BAC = m ang B'A'C', \ m ang ABC = m ang A'B'C', \ m ang ACB = m ang A'C'B'$
$m ang BAC = 1/3 m ang B'A'C', \ m ang ABC = 1/3 m ang A'B'C', \ m ang ACB = 1/3 m ang A'C'B'$

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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$Delta ABC$ undergoes the following sequence of transformations: a translation of 3 units right and 2 units down, a reflection over the x-axis, and a dilation of factor 3 centered at the origin. Which of the following points represent the vertices of the transformed triangle,

$Delta A'B'C' ?$

A'(-9,-2), B'(-18,6), and C'(-27,-9)
A'(9,1), B'(18,-3), and C'(27,3)
A'(9,3), B'(18,-6), and C'(27,9)
A'(-6,-12), B'(3,-12), and C'(12,-6)

Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

The coordinates of the vertices of

$Delta ABC$ are

$A(-9,7)$ ,

$B(-5,6)$ , and

$C(-7,2)$ . The coordinates of the vertices of

$Delta DEF$ are

$D(1/2,17/2)$ ,

$E(5/2, 8)$ , and

$F(3/2,6)$ . Which of the following sequences of transformations, applied to

$Delta ABC$ , shows that

$Delta ABC \ ~ \ Delta DEF ?$

A translation of 5 units left and 7 units down, a rotation of 270° counterclockwise about the origin, and then a dilation of factor $1/2$ centered at (1,3).
A translation of 1 unit right and 2 units down, a rotation of 180° counterclockwise about the origin, and then a dilation of factor $-1/2$ centered at (3,4).
A translation of 8 units right, a reflection over the y-axis, and then a dilation of factor $3/2$ centered at the origin.
A translation of 3 units right and 1 unit up, a rotation of 90° counterclockwise about the origin, and then a dilation of factor $1/2$ centered at (1,1).