Back to Exercise: Draw transformed figures

Exercises: Draw Transformed Figures and Specify Transformation Sequences

Show your work for each problem. When asked to draw a figure, list all image vertices with their coordinates.

Grade 9·21 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-co-a-5

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Warm-Up: Review What You Know

These problems review skills you have already learned.

Point $P$ has coordinates $(3, -2)$ . Under a translation by vector $(4, 5)$ , what are the coordinates of the image $P'$ ?

$(7, 3)$

$(-1, -7)$

$(7, -7)$

$(3, 3)$

Point $Q$ has coordinates $(-5, 2)$ . What are the coordinates of its image after a reflection over the $y$ -axis?

$(-5, -2)$

$(5, 2)$

$(2, -5)$

$(-2, 5)$

Point $R$ has coordinates $(4, 1)$ . What are the coordinates of its image after a $90^\circ$ counterclockwise rotation about the origin?

$(-1, 4)$

$(1, -4)$

$(-4, -1)$

$(4, -1)$

Fluency Practice

Apply the given transformation to each vertex. List all image coordinates.

$Triangle ABC on a coordinate grid with translation vector arrow (3, -2) shown at vertex A.$

Triangle $ABC$ has vertices $A(1, 2)$ , $B(4, 1)$ , and $C(3, 5)$ . It is translated by vector $(3, -2)$ .

Which set of coordinates gives the image $A'B'C'$ ?

$A'(4, 0)$ , $B'(7, -1)$ , $C'(6, 3)$

$A'(4, 0)$ , $B'(7, -1)$ , $C'(3, 5)$

$A'(-2, 4)$ , $B'(1, 3)$ , $C'(0, 7)$

$A'(4, 4)$ , $B'(7, 3)$ , $C'(6, 7)$

Quadrilateral $PQRS$ has vertices $P(0, 0)$ , $Q(4, 0)$ , $R(4, 3)$ , and $S(0, 3)$ . It is translated by vector $(-3, 2)$ .

What are the coordinates of $P'$ , $Q'$ , $R'$ , and $S'$ ?

$P'(-3, 2)$ , $Q'(1, 2)$ , $R'(1, 5)$ , $S'(-3, 5)$

$P'(3, -2)$ , $Q'(7, -2)$ , $R'(7, 1)$ , $S'(3, 1)$

$P'(-3, 2)$ , $Q'(1, 2)$ , $R'(4, 3)$ , $S'(0, 3)$

$P'(-3, 2)$ , $Q'(1, 2)$ , $R'(1, 3)$ , $S'(-3, 3)$

$Triangle DEF on a coordinate grid with the y-axis shown as the line of reflection.$

Triangle $DEF$ has vertices $D(-3, 1)$ , $E(0, 4)$ , and $F(2, -1)$ . It is reflected over the $y$ -axis.

What are the coordinates of the image $D'E'F'$ ?

$D'(3, 1)$ , $E'(0, 4)$ , $F'(-2, -1)$

$D'(-3, -1)$ , $E'(0, -4)$ , $F'(2, 1)$

$D'(1, -3)$ , $E'(4, 0)$ , $F'(-1, 2)$

$D'(3, 1)$ , $E'(0, 4)$ , $F'(2, -1)$

Triangle $GHK$ has vertices $G(1, 3)$ , $H(4, 3)$ , and $K(1, 7)$ . It is reflected over the horizontal line $y = 1$ .

What are the coordinates of the image $G'H'K'$ ?

$G'(1, -1)$ , $H'(4, -1)$ , $K'(1, -5)$

$G'(-1, 3)$ , $H'(-4, 3)$ , $K'(-1, 7)$

$G'(1, 3)$ , $H'(4, 3)$ , $K'(1, 7)$

$G'(1, 1)$ , $H'(4, 1)$ , $K'(1, -5)$

$Triangle LMN on a coordinate grid with a curved 90-degree counterclockwise rotation arrow shown centered at the origin.$

Triangle $LMN$ has vertices $L(2, 0)$ , $M(5, 0)$ , and $N(2, 4)$ . It is rotated $90^\circ$ counterclockwise about the origin.

What are the coordinates of the image $L'M'N'$ ?

$L'(0, 2)$ , $M'(0, 5)$ , $N'(-4, 2)$

$L'(0, -2)$ , $M'(0, -5)$ , $N'(4, -2)$

$L'(-2, 0)$ , $M'(-5, 0)$ , $N'(-2, -4)$

$L'(0, 2)$ , $M'(0, 5)$ , $N'(4, -2)$

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