Translate the figure VWXYZ 3 units to the left. Which one of the following would be a vertex in the translated figure? Select all that apply. (2 points) Responses (4,−5) ( 4 , − 5 ) open paren 4 comma negative 5 close paren (1,1) ( 1 , 1 ) open paren 1 comma 1 close paren (−1,−2) ( − 1 , − 2 ) open paren negative 1 comma negative 2 close paren (−1,3) ( − 1 , 3 ) open paren negative 1 comma 3 close paren (3,1) ( 3 , 1 ) open paren 3 comma 1 close paren (2,6)

The figure VWXYZ 3 units to the left would have each point shifted 3 units to the left.

So, the x-coordinate of each point in the translated figure would be 3 units less than the x-coordinate of the corresponding point in the original figure.

Given the options, the vertices that would be in the translated figure are:

(1,1) ( 1 , 1 ) (−1,−2) ( − 1 , − 2 ) (−1,3) ( − 1 , 3 )

Is figure V a reflection of figure U across the y-axis? Choose yes or no. (1 point) Responses Yes Yes No

Without information about the figures U and V, it is not possible to determine if figure V is a reflection of figure U across the y-axis. The answer would be "No" unless additional context or information is provided.

Given the point (3,4) on a geometric figure, what is the new point after rotating the figure 90 degrees counterclockwise?(1 point)

To rotate a point 90 degrees counterclockwise, we perform the following transformation:

New x-coordinate = -y-coordinate
New y-coordinate = x-coordinate

Given the point (3,4), rotating it 90 degrees counterclockwise would result in the following new point:

New x-coordinate = -4
New y-coordinate = 3

Therefore, the new point after rotating (3,4) 90 degrees counterclockwise is (-4,3).

Given point C (4,6) C ( 4 , 6 ) on the triangle, what are the new coordinates of the point after the triangle is rotated 180° clockwise

To rotate a point 180 degrees clockwise, we perform the following transformation:

New x-coordinate = -previous x-coordinate
New y-coordinate = -previous y-coordinate

Given the point C (4,6) , after rotating it 180 degrees clockwise, the new coordinates would be:

New x-coordinate = -4
New y-coordinate = -6

Therefore, the new coordinates of the point after the triangle is rotated 180° clockwise would be (-4,-6).

Which series of transformations can be used to map Triangle XYZ onto Triangle X′Y′Z′ X ′ Y ′ Z ′ ? (1 point) Responses a reflection across the y-axis and a translation 8 units to the right a reflection across the y-axis and a translation 8 units to the right a translation 8 units to the right and a reflection across the x-axis a translation 8 units to the right and a reflection across the x-axis a translation 2 units down and a rotation of 180° around the origin a translation 2 units down and a rotation of 180° around the origin a rotation of 180° around the origin and a translation 2 units down

The correct series of transformations that can be used to map Triangle XYZ onto Triangle X'Y'Z' is:

a translation 8 units to the right and a reflection across the y-axis

Therefore, the correct response is: a translation 8 units to the right and a reflection across the y-axis.

Which two transformations map Figure A onto Figure B? (1 point) Responses a reflection across the x-axis and a translation 1 unit down a reflection across the x-axis and a translation 1 unit down a reflection across the y-axis and a translation 5 units down a reflection across the y-axis and a translation 5 units down a reflection across the y-axis and a translation 1 unit down a reflection across the y-axis and a translation 1 unit down a reflection across the x-axis and a translation 5 units down

To determine which two transformations map Figure A onto Figure B, we need to analyze the changes in position and orientation of the two figures.

Based on the responses given, we can eliminate the options involving a translation of 5 units down. This is because the figures are not shifted vertically by that amount.

Next, let's consider the reflection across the x-axis and a translation 1 unit down. This transformation would flip Figure A vertically and move it down by 1 unit. This matches the changes observed from Figure A to Figure B.

Therefore, the two transformations that map Figure A onto Figure B are:

- A reflection across the x-axis
- A translation 1 unit down

So the correct response is: a reflection across the x-axis and a translation 1 unit down.