A line containing the points (−2, 3) and (2, 3) is reflected across the x -axis. How long is the reflected line?(1 point)
Responses
not enough information
not enough information
infinitely long
infinitely long
3 units
3 units
4 units
The line that is reflected across the x-axis will have the same length as the original line. Therefore, the length of the reflected line is 4 units.
A line segment has endpoints (2,−1) and (5, −4). What are the new endpoints after rotating the segment 90° clockwise?(1 point)
Responses
(−1, −2) and (−4, −5)
left parenthesis negative 1 comma negative 2 right parenthesis and left parenthesis negative 4 comma negative 5 right parenthesis
(−2, −1) and (−5, −4)
left parenthesis negative 2 comma negative 1 right parenthesis and left parenthesis negative 5 comma negative 4 right parenthesis
(−2, 1) and (−5, 4)
left parenthesis negative 2 comma 1 right parenthesis and left parenthesis negative 5 comma 4 right parenthesis
(2, −1) and (4, 5)
To rotate a point 90° clockwise, we switch the x and y coordinates and negate the new x coordinate.
For the first point (2, -1), the new x coordinate is -1, and the new y coordinate is 2. So the new endpoint is (-1, 2).
For the second point (5, -4), the new x coordinate is -4, and the new y coordinate is 5. So the new endpoint is (-4, 5).
Therefore, the new endpoints after rotating the segment 90° clockwise are (-1, 2) and (-4, 5).
A rectangle has a side that is 10 units long. How long will this side be after the figure is translated down 4 units and to the right 5 units?(1 point)
units
After translating the rectangle down 4 units, the length of the side will remain the same at 10 units.
After translating the rectangle to the right 5 units, the length of the side will also remain the same at 10 units.
Therefore, the length of the side will still be 10 units after the figure is translated down 4 units and to the right 5 units.
A rectangle has a side that is 10 units long. How long will this side be after the figure is translated down 4 units and to the right 5 units?
units
The length of the side of the rectangle will remain the same after translating it down 4 units and to the right 5 units. Therefore, the length of the side will still be 10 units.
Use the image to answer the question.
An illustration of a coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A pentagon upper H upper I upper J upper K upper L is plotted on the graph with the vertices marked as closed points. The vertices of the pentagon upper H upper I upper J upper K upper L are marked at upper H left parenthesis negative 3 comma 6 right parenthesis, upper I left parenthesis negative 1 comma 4 right parenthesis, upper J left parenthesis negative 1 comma 1 right parenthesis, upper K left parenthesis negative 4 comma 1 right parenthesis, and upper L left parenthesis negative 5 comma 4 right parenthesis.
Translate the figure HIJKL 3 units to the left. Which of the following would be a vertex in the translated figure?
(1 point)
Responses
(−7, 4)
left parenthesis negative 7 comma 4 right parenthesis
(−1, −2)
left parenthesis negative 1 comma negative 2 right parenthesis
(−6, 6)
left parenthesis negative 6 comma 6 right parenthesis
(2, 4)
To translate the figure HIJKL 3 units to the left, we subtract 3 from the x-coordinate of each vertex.
The original vertices are:
H: (-3, 6)
I: (-1, 4)
J: (-1, 1)
K: (-4, 1)
L: (-5, 4)
After translating 3 units to the left, the new vertices will be:
H: (-3 - 3, 6) = (-6, 6)
I: (-1 - 3, 4) = (-4, 4)
J: (-1 - 3, 1) = (-4, 1)
K: (-4 - 3, 1) = (-7, 1)
L: (-5 - 3, 4) = (-8, 4)
Therefore, the vertex in the translated figure is (-6, 6).
Triangle XYZ is translated down 4 units and to the left 8 units. The length of side XY is 10 units. What is the length of side X′Y′?(1 point)
units
After translating Triangle XYZ down 4 units and to the left 8 units, the length of side XY remains the same at 10 units. The translation does not affect the length of the sides.
Therefore, the length of side X'Y' will also be 10 units.