Quiz about 8th grade Ch 6 L2

Question 1

The figure is reflected over the y-axis. Find the coordinates of point A' and point B'. Then sketch the image on the coordinate plane.

Accepted Answer

The coordinates of A' are (-4, 4) and the coordinates of B' are (-2, 1).

Answer

The coordinates of A' are (4, 4) and the coordinates of B' are (2, 1).

Answer

The coordinates of A' are (-4, -4) and the coordinates of B' are (-2, -1).

Answer

The coordinates of A' are (4, -4) and the coordinates of B' are (2, -1).

Question 2

To determine the coordinates of a figure after a reflection over either axis, you must:

Accepted Answer

Change the sign of the appropriate coordinate depending on the axis of reflection.

Answer

Add 1 to both coordinates.

Answer

Multiply both coordinates by 2.

Answer

Switch the x- and y-coordinates.

Question 3

Graph each figure and its reflection over the indicated axis. Then find the coordinates of the reflected image. Quadrilateral WXYZ with vertices W(-1, -1), X(4, 1), Y(4, 5), and Z(1, 7) over the x-axis.

Accepted Answer

W'(-1, 1), X'(4, -1), Y'(4, -5), Z'(1, -7)

Answer

W'(-1, -1), X'(4, 1), Y'(4, 5), Z'(1, 7)

Answer

W'(-1, -1), X'(4, -1), Y'(4, -5), Z'(1, -7)

Answer

W'(-1, 1), X'(4, 1), Y'(4, 5), Z'(1, 7)

Question 4

Graph each figure and its reflection over the indicated axis. Then find the coordinates of the reflected image. Quadrilateral DEFG with vertices D(1, 0), E(1, -5), F(4, -1), and G(3, 2) over the y-axis.

Accepted Answer

D'(-1, 0), E'(-1, -5), F'(-4, -1), G'(-3, 2)

Answer

D'(1, 0), E'(1, 5), F'(4, 1), G'(3, -2)

Answer

D'(-1, 0), E'(-1, 5), F'(-4, 1), G'(-3, -2)

Answer

D'(0, 1), E'(0, -5), F'(1, -4), G'(2, -3)

Question 5

The figure at the right is reflected over the x-axis. Find the coordinates of point A' and point B'. Then sketch the image on the coordinate plane.

Accepted Answer

A'(1, -7), B'(8, -7)

Answer

A'(1, 7), B'(8, 7)

Answer

A'(-1, -7), B'(-8, -7)

Answer

A'(1, -8), B'(7, -8)

Question 6

Roberto is finding the coordinates of the image of a triangle with vertices A(1, 1), B(4, 1) and C(1, 5) after a reflection over the x-axis. What is his mistake and how should it be corrected?

Accepted Answer

He reflected over the y-axis instead of the x-axis; he should change the sign of the y-coordinates, not the x-coordinates.

Answer

He did not change any coordinates; he should reflect each point over the x-axis by changing the sign of the y-coordinates.

Answer

He added instead of subtracting the coordinates; he should only change the sign of the y-coordinates.

Answer

He reflected over the origin; he should only reflect over the x-axis by changing the sign of the y-coordinates.

Question 7

Triangle JKL has vertices J(-7, 4), K(7, 1), and L(2, -2). Without graphing, find the new coordinates of the vertices of the triangle after a reflection first over the x-axis and then over the y-axis.

Accepted Answer

J(7, -4), K(-7, -1), L(-2, 2)

Answer

J(-7, -4), K(7, -1), L(2, 2)

Answer

J(7, 4), K(-7, 1), L(-2, -2)

Answer

J(-7, 4), K(7, -1), L(2, -2)

Question 8

Suppose you reflect a triangle in Quadrant I over the y-axis, then translate the image 2 units left and 3 units down. Is there a single transformation that maps the preimage onto the image?

Accepted Answer

Yes, a single glide reflection can map the preimage onto the image.

Answer

No, it requires at least two separate transformations.

Answer

Yes, a single rotation can achieve this mapping.

Answer

Yes, a single dilation can achieve this mapping.

Question 9

Suppose you reflect a nonregular figure over the x-axis and then reflect it over the y-axis. Is there a single transformation using reflections or translations that maps the preimage onto the image?

Accepted Answer

Yes, a rotation of 180 degrees about the origin will map the preimage onto the image.

Answer

No, there is no single transformation that can achieve this.

Answer

Yes, a translation along the x-axis will map the preimage onto the image.

Answer

Yes, a reflection over the line y = x will map the preimage onto the image.

Question 10

Which One Doesn't Belong? Triangle ABC has vertices A(1, 2), B(1, 5), and C(4, 2) and undergoes a transformation. Circle the set of vertices that does not belong. Explain your reasoning.

Accepted Answer

A'(5, 2), B'(5, 5), C'(8, 2)

Answer

A'(1, -1), B'(1, 2), C'(4, -1)

Answer

A'(1, 2), B'(1, -5), C'(4, 2)

Answer

A'(1, -2), B'(1, -5), C'(4, -2)

Question 11

Graph the image of triangle RST after it is reflected over the x-axis then translated 4 units to the right and 3 units down. What are the vertices of triangle R'S'T'?

Accepted Answer

The vertices of triangle R'S'T' are (3, -6), (6, -5), and (4, -8).

Answer

The vertices of triangle R'S'T' are (3, 6), (6, 5), and (4, 8).

Answer

The vertices of triangle R'S'T' are (-3, -6), (-6, -5), (-4, -8).

Answer

The vertices of triangle R'S'T' are (7, -2), (10, -1), and (8, -4).

Question 12

The figure shown at the right was transformed from Quadrant II to Quadrant III. Fill in each box to make a true statement to describe the transformation. The figure was reflected over the x-axis.

Accepted Answer

reflected, x-axis

Answer

rotated, y-axis

Answer

translated, x-axis

Answer

reflected, y-axis

8th grade Ch 6 L2

27 questions

Graph △ABC with vertices A(5, 1), B(1, 2), and C(6, 2) and its reflection over the x-axis. Then find the coordinates of the image.

The figure is reflected over the y-axis. Find the coordinates of point A' and point B'. Then sketch the image on the coordinate plane.

To determine the coordinates of a figure after a reflection over either axis, you must:

Graph each figure and its reflection over the indicated axis. Then find the coordinates of the reflected image. ΔGHJ with vertices G(4, 2), H(3, -4), and J(1, 1) over the y-axis. What are the coordinates of the reflected image?

Graph each figure and its reflection over the indicated axis. Then find the coordinates of the reflected image. ΔMNP with vertices M(2, 1), N(-3, 1), and P(-1, 4) over the x-axis. What are the coordinates of the reflected image?

Graph each figure and its reflection over the indicated axis. Then find the coordinates of the reflected image. Quadrilateral WXYZ with vertices W(-1, -1), X(4, 1), Y(4, 5), and Z(1, 7) over the x-axis.

Graph each figure and its reflection over the indicated axis. Then find the coordinates of the reflected image. Quadrilateral DEFG with vertices D(1, 0), E(1, -5), F(4, -1), and G(3, 2) over the y-axis.

The figure at the right is reflected over the x-axis. Find the coordinates of point A' and point B'. Then sketch the image on the coordinate plane.

The coordinates of a point and its image after a reflection are given. Describe the reflection as over the x-axis or y-axis. A(-3, 5) → A'(3, 5)

The coordinates of a point and its image after a reflection are given. Describe the reflection as over the x-axis or y-axis. M(3, 3) → M'(3, -3)

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