Draw ∠ R S T \angle RST ∠ R S T . What is the name of one of the sides of ∠ R S T \angle RST ∠ R S T ?

S T → \overrightarrow{ST} S T <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

R S → \overrightarrow{RS} R S <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z">

Rotate the triangle R ( 3 , 1 ) R\left(3,\ 1\right) R ( 3 , 1 ) , S ( 1 , 3 ) S\left(1,\ 3\right) S ( 1 , 3 ) , T ( 4 , 5 ) T\left(4,\ 5\right) T ( 4 , 5 ) 180 ° 180\degree 1 8 0 ° about the origin.

R ′ ( − 3 , − 1 ) , S ′ ( − 1 , − 3 ) , T ′ ( − 4 , − 5 ) R'\left(-3,\ -1\right),\ S'\left(-1,\ -3\right),\ T'\left(-4,\ -5\right) R ′ ( − 3 , − 1 ) , S ′ ( − 1 , − 3 ) , T ′ ( − 4 , − 5 )

R ′ ( 1 , 3 ) , S ′ ( 3 , 1 ) , T ′ ( 5 , 4 ) R'\left(1,\ 3\right),\ S'\left(3,\ 1\right),\ T'\left(5,\ 4\right) R ′ ( 1 , 3 ) , S ′ ( 3 , 1 ) , T ′ ( 5 , 4 )

R ′ ( − 1 , − 3 ) , S ′ ( − 3 , − 1 ) , T ′ ( − 5 , − 4 ) R'\left(-1,\ -3\right),\ S'\left(-3,\ -1\right),\ T'\left(-5,\ -4\right) R ′ ( − 1 , − 3 ) , S ′ ( − 3 , − 1 ) , T ′ ( − 5 , − 4 )

R ′ ( 3 , 1 ) , S ′ ( 1 , − 3 ) , T ′ ( 4 , − 5 ) R'\left(3,\ 1\right),\ S'\left(1,\ -3\right),\ T'\left(4,\ -5\right) R ′ ( 3 , 1 ) , S ′ ( 1 , − 3 ) , T ′ ( 4 , − 5 )

Reflect the triangle T ( − 1 , − 2 ) , U ( 1 , 1 ) , V ( 4 , − 3 ) T\left(-1,\ -2\right),\ U\left(1,\ 1\right),\ V\left(4,\ -3\right) T ( − 1 , − 2 ) , U ( 1 , 1 ) , V ( 4 , − 3 ) across the line y=x y = x .

T ′ ( − 2 , − 1 ) , U ′ ( 1 , 1 ) , V ′ ( − 3 , 4 ) T'\left(-2,\ -1\right),\ U'\left(1,\ 1\right),\ V'\left(-3,\ 4\right) T ′ ( − 2 , − 1 ) , U ′ ( 1 , 1 ) , V ′ ( − 3 , 4 )

T ′ ( 1 , − 2 ) , U ′ ( − 1 , − 1 ) , V ′ ( − 4 , − 3 ) T'\left(1,\ -2\right),\ U'\left(-1,\ -1\right),\ V'\left(-4,\ -3\right) T ′ ( 1 , − 2 ) , U ′ ( − 1 , − 1 ) , V ′ ( − 4 , − 3 )

T ′ ( − 1 , 2 ) , U ′ ( 1 , 1 ) , V ′ ( 4 , 3 ) T'\left(-1,\ 2\right),\ U'\left(1,\ 1\right),\ V'\left(4,\ 3\right) T ′ ( − 1 , 2 ) , U ′ ( 1 , 1 ) , V ′ ( 4 , 3 )

T ′ ( 1 , 2 ) , U ′ ( − 1 , 1 ) , V ′ ( − 4 , 3 ) T'\left(1,\ 2\right),\ U'\left(-1,\ 1\right),\ V'\left(-4,\ 3\right) T ′ ( 1 , 2 ) , U ′ ( − 1 , 1 ) , V ′ ( − 4 , 3 )

Reflecting over which line will map the rhombus onto itself?

y = 1 4 x y=\frac{1}{4}x y = 4 1 x

What are the endpoints of the image A ′ B ′ ‾ \overline{A'B'} A ′ B ′ if A B ‾ \overline{AB} A B is reflected about the line y = x y=x y = x ?

A ′ ( − 3 , 2 ) , B ′ ( − 7 , 4 ) A'\left(-3,\ 2\right),\ B'\left(-7,\ 4\right) A ′ ( − 3 , 2 ) , B ′ ( − 7 , 4 )

A ′ ( 2 , 3 ) , B ′ ( 4 , 7 ) A'\left(2,\ 3\right),\ B'\left(4,\ 7\right) A ′ ( 2 , 3 ) , B ′ ( 4 , 7 )

A ′ ( − 2 , − 3 ) , B ′ ( − 4 , − 7 ) A'\left(-2,\ -3\right),\ B'\left(-4,\ -7\right) A ′ ( − 2 , − 3 ) , B ′ ( − 4 , − 7 )

A ′ ( 3 , − 2 ) , B ′ ( 7 , − 4 ) A'\left(3,\ -2\right),\ B'\left(7,\ -4\right) A ′ ( 3 , − 2 ) , B ′ ( 7 , − 4 )

The vertices of Δ R S T \Delta RST Δ R S T are R ( 1 , − 1 ) , S ( 4 , 1 ) , a n d T ( 4 , − 3 ) R\left(1,\ -1\right),\ S\left(4,\ 1\right),\ and\ T\left(4,\ -3\right) R ( 1 , − 1 ) , S ( 4 , 1 ) , a n d T ( 4 , − 3 ) . What are the coordinates of the image after a 90 ° 90\degree 9 0 ° rotation about the origin?

R ′ ( 1 , 1 ) , S ′ ( − 1 , 4 ) , T ′ ( 3 , 4 ) R'\left(1,\ 1\right),\ S'\left(-1,\ 4\right),\ T'\left(3,\ 4\right) R ′ ( 1 , 1 ) , S ′ ( − 1 , 4 ) , T ′ ( 3 , 4 )

R ′ ( − 1 , 1 ) , S ′ ( − 4 , − 1 ) , T ′ ( − 4 , 3 ) R'\left(-1,\ 1\right),\ S'\left(-4,\ -1\right),\ T'\left(-4,\ 3\right) R ′ ( − 1 , 1 ) , S ′ ( − 4 , − 1 ) , T ′ ( − 4 , 3 )

R ′ ( 1 , − 1 ) , S ′ ( − 1 , − 4 ) , T ′ ( 3 , − 4 ) R'\left(1,\ -1\right),\ S'\left(-1,\ -4\right),\ T'\left(3,\ -4\right) R ′ ( 1 , − 1 ) , S ′ ( − 1 , − 4 ) , T ′ ( 3 , − 4 )

R ′ ( − 1 , − 1 ) , S ′ ( − 1 , − 4 ) , T ′ ( − 3 , − 4 ) R'\left(-1,\ -1\right),\ S'\left(-1,\ -4\right),\ T'\left(-3,\ -4\right) R ′ ( − 1 , − 1 ) , S ′ ( − 1 , − 4 ) , T ′ ( − 3 , − 4 )

Which statement describes the image?

Rotation of 180 ° 180\degree 1 8 0 ° about the origin

Reflection of the line y = x y=x y = x

Rotation of 180 ° 180\degree 1 8 0 ° about the point ( − 1 , 1 ) \left(-1,\ 1\right) ( − 1 , 1 )

Translation right two units, down 2 units

Which reflection, or composition of reflections, always produces the same image as a rotation 180 degrees about the origin?

A reflection over the x-axis followed by a reflection of that image over the y-axis.

A reflection over the line y = x.

A reflection over the x-axis followed by a reflection of that image over the x-axis.

A reflection over a line that bisects the figure.

Given a point in the coordinate plane, the rule ( x , y ) → ( x + 2 , y − 3 ) \left(x,\ y\right)\rightarrow\left(x+2,\ y-3\right) ( x , y ) → ( x + 2 , y − 3 ) translates the point in which direction?

2 units to the right and 3 units down

2 units to the left and 3 units up

3 units to the left and 2 units down

3 units to the right and 2 units up

The preimage for a reflection is shaded. Which represents the mapping?

B C D A → F E H G BCDA\rightarrow FEHG B C D A → F E H G

A B C D → H E F G ABCD\rightarrow HEFG A B C D → H E F G

G H E F → A C D B GHEF\rightarrow ACDB G H E F → A C D B

D A B C → F G H E DABC\rightarrow FGHE D A B C → F G H E

Which vector translates R to S ?

< − 3 , 5 > <-3,\ 5> < − 3 , 5 >

< − 3 , − 5 > <-3,\ -5> < − 3 , − 5 >

< 3 , − 5 > <3,\ -5> < 3 , − 5 >

< − 5 , 3 > <-5,\ 3> < − 5 , 3 >

Δ D E F \Delta DEF Δ D E F with vertices D ( 1 , 2 ) , E ( 3 , 4 ) , a n d F ( 1 , 4 ) D\left(1,\ 2\right),\ E\left(3,\ 4\right),\ and\ F\left(1,\ 4\right) D ( 1 , 2 ) , E ( 3 , 4 ) , a n d F ( 1 , 4 ) is reflected across the y-axis, and then its image is reflected across the line y = x y=x y = x . Which single transformation moves the triangle from its starting position to its final position?

Rotation by 270 ° 270\degree 2 7 0 ° counter-clockwise about the origin

Rotation by 90 ° 90\degree 9 0 ° counter-clockwise about the origin

Coordinate Algebra Unit 5 EOC Review

Authored by Bailey Kirk

Mathematics

9th Grade

CCSS covered

Used 52+ times

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33 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which segment is perpendicular to $\overline{DE}$ ?

$\overline{AB}$

$\overline{CF}$

$\overline{DF}$

$\overline{EF}$

Tags

CCSS.HSG.CO.A.1

CCSS.4.G.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Classify $\overline{EH}$ and $\overline{DH}$ .

Skew segments

Parallel segments

Perpendicular segments

Parallel planes

Tags

CCSS.HSG.CO.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Which angle measures approximately $72\degree$ ?

Tags

CCSS.4.MD.C.6

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Draw $\angle RST$ . What is the name of one of the sides of $\angle RST$ ?

$\overrightarrow{RS}$

$\overrightarrow{ST}$

$\overline{RS}$

$\overline{ST}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Rotate the triangle $R\left(3,\ 1\right)$ , $S\left(1,\ 3\right)$ , $T\left(4,\ 5\right)$ $180\degree$ about the origin.

$R'\left(1,\ 3\right),\ S'\left(3,\ 1\right),\ T'\left(5,\ 4\right)$

$R'\left(-1,\ -3\right),\ S'\left(-3,\ -1\right),\ T'\left(-5,\ -4\right)$

$R'\left(-3,\ -1\right),\ S'\left(-1,\ -3\right),\ T'\left(-4,\ -5\right)$

$R'\left(3,\ 1\right),\ S'\left(1,\ -3\right),\ T'\left(4,\ -5\right)$

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What are the coordinates of the image of $\left(-3,\ 2\right)$ when the point is reflected across the line $y=4$ ?

(-3, 4)

(-1, 6)

(6, -3)

(-3, 6)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Translate the quadrilateral $W\left(-2,\ 2\right),\ X\left(-3,\ 3\right),\ Y\left(-6,\ 5\right),\ Z\left(-6,\ 3\right)$ using the transformation $\left(x-2,\ y+3\right)$ .

$W'\left(-4,\ 5\right),\ X'\left(-5,\ 6\right),\ Y'\left(-8,\ 8\right),\ Z'\left(-8,\ 6\right)$

$W'\left(0,\ 5\right),\ X'\left(-1,\ 6\right),\ Y'\left(-4,\ 8\right),\ Z'\left(-4,\ 6\right)$

$W'\left(0,\ -1\right),\ X'\left(-1,\ 0\right),\ Y'\left(-4,\ 2\right),\ Z'\left(-4,\ 0\right)$

$W'\left(4,\ 6\right),\ X'\left(6,\ 9\right),\ Y'\left(12,\ 15\right),\ Z'\left(12,\ 9\right)$

Tags

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Reflect the triangle $T\left(-1,\ -2\right),\ U\left(1,\ 1\right),\ V\left(4,\ -3\right)$ across the line $y=x$ .

$T'\left(1,\ -2\right),\ U'\left(-1,\ -1\right),\ V'\left(-4,\ -3\right)$

$T'\left(-1,\ 2\right),\ U'\left(1,\ 1\right),\ V'\left(4,\ 3\right)$

$T'\left(1,\ 2\right),\ U'\left(-1,\ 1\right),\ V'\left(-4,\ 3\right)$

$T'\left(-2,\ -1\right),\ U'\left(1,\ 1\right),\ V'\left(-3,\ 4\right)$

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Rotate $\Delta RSQ$ with vertices $R\left(4,\ -1\right),\ S\left(5,\ 3\right),\ and\ Q\left(3,\ 1\right)$ by $90\degree$ about the origin.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$\Delta ABC$ has vertices $A\left(3,\ 1\right),\ B\left(4,\ 5\right),\ and\ C\left(2,\ 3\right)$ . Rotate $\Delta ABC\ 90\degree$ counterclockwise about the origin and then reflect it across the x-axis.

Tags

CCSS.8.G.A.3

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Coordinate Algebra Unit 5 EOC Review

Which segment is perpendicular to DE‾\overline{DE}DE ?

Classify EH‾\overline{EH}EH and DH‾\overline{DH}DH .

Which angle measures approximately 72°72\degree72° ?

Draw ∠RST\angle RST∠RST . What is the name of one of the sides of ∠RST\angle RST∠RST ?

Rotate the triangle R(3, 1)R\left(3,\ 1\right)R(3, 1) , S(1, 3)S\left(1,\ 3\right)S(1, 3) , T(4, 5)T\left(4,\ 5\right)T(4, 5) 180°180\degree180° about the origin.

What are the coordinates of the image of (−3, 2)\left(-3,\ 2\right)(−3, 2) when the point is reflected across the line y=4y=4y=4 ?

Translate the quadrilateral W(−2, 2), X(−3, 3), Y(−6, 5), Z(−6, 3)W\left(-2,\ 2\right),\ X\left(-3,\ 3\right),\ Y\left(-6,\ 5\right),\ Z\left(-6,\ 3\right)W(−2, 2), X(−3, 3), Y(−6, 5), Z(−6, 3) using the transformation (x−2, y+3)\left(x-2,\ y+3\right)(x−2, y+3) .

Reflect the triangle T(−1, −2), U(1, 1), V(4, −3)T\left(-1,\ -2\right),\ U\left(1,\ 1\right),\ V\left(4,\ -3\right)T(−1, −2), U(1, 1), V(4, −3) across the line y=xy=x .

Rotate ΔRSQ\Delta RSQΔRSQ with vertices R(4, −1), S(5, 3), and Q(3, 1)R\left(4,\ -1\right),\ S\left(5,\ 3\right),\ and\ Q\left(3,\ 1\right)R(4, −1), S(5, 3), and Q(3, 1) by 90°90\degree90° about the origin.

ΔABC\Delta ABCΔABC has vertices A(3, 1), B(4, 5), and C(2, 3)A\left(3,\ 1\right),\ B\left(4,\ 5\right),\ and\ C\left(2,\ 3\right)A(3, 1), B(4, 5), and C(2, 3) . Rotate ΔABC 90°\Delta ABC\ 90\degreeΔABC 90° counterclockwise about the origin and then reflect it across the x-axis.

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Which segment is perpendicular to $\overline{DE}$ ?

Classify $\overline{EH}$ and $\overline{DH}$ .

Which angle measures approximately $72\degree$ ?

Draw $\angle RST$ . What is the name of one of the sides of $\angle RST$ ?

Rotate the triangle $R\left(3,\ 1\right)$ , $S\left(1,\ 3\right)$ , $T\left(4,\ 5\right)$ $180\degree$ about the origin.

What are the coordinates of the image of $\left(-3,\ 2\right)$ when the point is reflected across the line $y=4$ ?

Translate the quadrilateral $W\left(-2,\ 2\right),\ X\left(-3,\ 3\right),\ Y\left(-6,\ 5\right),\ Z\left(-6,\ 3\right)$ using the transformation $\left(x-2,\ y+3\right)$ .

Reflect the triangle $T\left(-1,\ -2\right),\ U\left(1,\ 1\right),\ V\left(4,\ -3\right)$ across the line $y=x$ .

Rotate $\Delta RSQ$ with vertices $R\left(4,\ -1\right),\ S\left(5,\ 3\right),\ and\ Q\left(3,\ 1\right)$ by $90\degree$ about the origin.

$\Delta ABC$ has vertices $A\left(3,\ 1\right),\ B\left(4,\ 5\right),\ and\ C\left(2,\ 3\right)$ . Rotate $\Delta ABC\ 90\degree$ counterclockwise about the origin and then reflect it across the x-axis.