Please answer the question below.
Reflect the endpoint of a line segment (−5, 10) across the x -axis. What is the result?
11 answers
The result of reflecting the endpoint (−5, 10) across the x -axis is the point (−5, -10).
Please answer the question below.
Demonstrate the translation of a line segment of 3 units to the left and 5 units down if the endpoints of the line segment are (−2, 7) and (0, 3) .
Demonstrate the translation of a line segment of 3 units to the left and 5 units down if the endpoints of the line segment are (−2, 7) and (0, 3) .
To translate a line segment 3 units to the left and 5 units down, we subtract 3 from the x-coordinates and subtract 5 from the y-coordinates of the endpoints.
Endpoint 1: (-2, 7)
To translate 3 units to the left: -2 - 3 = -5
To translate 5 units down: 7 - 5 = 2
So the translated endpoint 1 is (-5, 2).
Endpoint 2: (0, 3)
To translate 3 units to the left: 0 - 3 = -3
To translate 5 units down: 3 - 5 = -2
So the translated endpoint 2 is (-3, -2).
Therefore, the translated line segment has endpoints (-5, 2) and (-3, -2).
Endpoint 1: (-2, 7)
To translate 3 units to the left: -2 - 3 = -5
To translate 5 units down: 7 - 5 = 2
So the translated endpoint 1 is (-5, 2).
Endpoint 2: (0, 3)
To translate 3 units to the left: 0 - 3 = -3
To translate 5 units down: 3 - 5 = -2
So the translated endpoint 2 is (-3, -2).
Therefore, the translated line segment has endpoints (-5, 2) and (-3, -2).
Please answer the question below.
If a line segment with endpoints (6, 3) and (6, 7) is translated 3 units up and 4 units to the right, how long is the line segment after the translation?
If a line segment with endpoints (6, 3) and (6, 7) is translated 3 units up and 4 units to the right, how long is the line segment after the translation?
To translate the line segment 3 units up and 4 units to the right, we add 3 to the y-coordinates and add 4 to the x-coordinates of the endpoints.
Endpoint 1: (6, 3)
To translate 3 units up: 3 + 3 = 6
To translate 4 units to the right: 6 + 4 = 10
So the translated endpoint 1 is (10, 6).
Endpoint 2: (6, 7)
To translate 3 units up: 7 + 3 = 10
To translate 4 units to the right: 6 + 4 = 10
So the translated endpoint 2 is (10, 10).
By the distance formula, the length of the line segment can be calculated as follows:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((10 - 10)^2 + (10 - 6)^2)
d = √(0 + 16)
d = √16
d = 4
Therefore, the length of the line segment after the translation is 4 units.
Endpoint 1: (6, 3)
To translate 3 units up: 3 + 3 = 6
To translate 4 units to the right: 6 + 4 = 10
So the translated endpoint 1 is (10, 6).
Endpoint 2: (6, 7)
To translate 3 units up: 7 + 3 = 10
To translate 4 units to the right: 6 + 4 = 10
So the translated endpoint 2 is (10, 10).
By the distance formula, the length of the line segment can be calculated as follows:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((10 - 10)^2 + (10 - 6)^2)
d = √(0 + 16)
d = √16
d = 4
Therefore, the length of the line segment after the translation is 4 units.
Please answer the question below.
A line segment has endpoints (1, 1) and (4, 4) . Demonstrating the properties of reflections across the y -axis, what are the reflected endpoints?
A line segment has endpoints (1, 1) and (4, 4) . Demonstrating the properties of reflections across the y -axis, what are the reflected endpoints?
To reflect a point across the y-axis, we change the sign of its x-coordinate while keeping the y-coordinate the same.
Endpoint 1: (1, 1)
When reflected across the y-axis: (-1, 1)
Endpoint 2: (4, 4)
When reflected across the y-axis: (-4, 4)
Therefore, the reflected endpoints of the line segment (1, 1) and (4, 4) across the y-axis are (-1, 1) and (-4, 4), respectively.
Endpoint 1: (1, 1)
When reflected across the y-axis: (-1, 1)
Endpoint 2: (4, 4)
When reflected across the y-axis: (-4, 4)
Therefore, the reflected endpoints of the line segment (1, 1) and (4, 4) across the y-axis are (-1, 1) and (-4, 4), respectively.
Please answer the question below.
A line contains the points (6,−3) and (3, 1) . When this line is reflected across the y -axis, what are the two new points?
A line contains the points (6,−3) and (3, 1) . When this line is reflected across the y -axis, what are the two new points?
To reflect a point across the y-axis, we change the sign of its x-coordinate while keeping the y-coordinate the same.
Endpoint 1: (6, -3)
When reflected across the y-axis: (-6, -3)
Endpoint 2: (3, 1)
When reflected across the y-axis: (-3, 1)
Therefore, the two new points after reflecting the line across the y-axis are (-6, -3) and (-3, 1).
Endpoint 1: (6, -3)
When reflected across the y-axis: (-6, -3)
Endpoint 2: (3, 1)
When reflected across the y-axis: (-3, 1)
Therefore, the two new points after reflecting the line across the y-axis are (-6, -3) and (-3, 1).
Please answer the question below.
A line segment has endpoints (0, 5) and (6, 5) . After the line segment is reflected across the x -axis, how long will it be?
A line segment has endpoints (0, 5) and (6, 5) . After the line segment is reflected across the x -axis, how long will it be?
When a line segment is reflected across the x-axis, the y-coordinates of the endpoints are negated while the x-coordinates remain the same.
Endpoint 1: (0, 5)
After reflecting across the x-axis: (0, -5)
Endpoint 2: (6, 5)
After reflecting across the x-axis: (6, -5)
To find the length of the line segment, we can calculate the distance between the reflected endpoints using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((6 - 0)^2 + (-5 - (-5))^2)
d = √(36 + 0)
d = √36
d = 6
Therefore, the length of the line segment after reflecting across the x-axis is 6 units.
Endpoint 1: (0, 5)
After reflecting across the x-axis: (0, -5)
Endpoint 2: (6, 5)
After reflecting across the x-axis: (6, -5)
To find the length of the line segment, we can calculate the distance between the reflected endpoints using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((6 - 0)^2 + (-5 - (-5))^2)
d = √(36 + 0)
d = √36
d = 6
Therefore, the length of the line segment after reflecting across the x-axis is 6 units.
2 answers