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