To find the reflected endpoints across the y-axis, we need to change the sign of the x-coordinates and keep the sign of the y-coordinates the same.
The given endpoints are (1,1) and (4,4).
For the first endpoint (1,1):
- Reflecting it across the y-axis, the x-coordinate changes its sign: 1 becomes -1.
- The y-coordinate remains the same: 1 remains 1.
- The reflected endpoint across the y-axis is (-1,1).
For the second endpoint (4,4):
- Reflecting it across the y-axis, the x-coordinate changes its sign: 4 becomes -4.
- The y-coordinate remains the same: 4 remains 4.
- The reflected endpoint across the y-axis is (-4,4).
Therefore, the reflected endpoints across the y-axis are (-1,1) and (-4,4).
A line segment has endpoints (1,1) and (4,4). Demonstrating the properties of reflections across the y-axis, what are reflected endpoints
5 answers
A line contains the points (6,-3) and (3,1) when the line is reflected across the y-axis, what are the two new points?
To find the new points after reflecting a line across the y-axis, we need to change the sign of the x-coordinates and keep the sign of the y-coordinates the same.
The given points are (6, -3) and (3, 1).
For the first point (6, -3):
- Reflecting it across the y-axis, the x-coordinate changes its sign: 6 becomes -6.
- The y-coordinate remains the same: -3 remains -3.
- The new point after reflection is (-6, -3).
For the second point (3, 1):
- Reflecting it across the y-axis, the x-coordinate changes its sign: 3 becomes -3.
- The y-coordinate remains the same: 1 remains 1.
- The new point after reflection is (-3, 1).
Therefore, the two new points after reflecting the line (6, -3) and (3, 1) across the y-axis are (-6, -3) and (-3, 1).
The given points are (6, -3) and (3, 1).
For the first point (6, -3):
- Reflecting it across the y-axis, the x-coordinate changes its sign: 6 becomes -6.
- The y-coordinate remains the same: -3 remains -3.
- The new point after reflection is (-6, -3).
For the second point (3, 1):
- Reflecting it across the y-axis, the x-coordinate changes its sign: 3 becomes -3.
- The y-coordinate remains the same: 1 remains 1.
- The new point after reflection is (-3, 1).
Therefore, the two new points after reflecting the line (6, -3) and (3, 1) across the y-axis are (-6, -3) and (-3, 1).
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 change their signs while the x-coordinates remain the same.
The given endpoints are (0, 5) and (6, 5).
After reflecting across the x-axis:
- The y-coordinate of the first endpoint (0, 5) changes sign: 5 becomes -5.
- The x-coordinate remains the same: 0 remains 0.
- The reflected endpoint is (0, -5).
Similarly,
- The y-coordinate of the second endpoint (6, 5) changes sign: 5 becomes -5.
- The x-coordinate remains the same: 6 remains 6.
- The reflected endpoint is (6, -5).
Therefore, the reflected line segment has endpoints (0, -5) and (6, -5).
The length of the line segment can be found by subtracting the x-coordinates of the endpoints. In this case, the x-coordinates of both endpoints are the same, which means the line segment has a length of 6 - 0 = 6 units.
The given endpoints are (0, 5) and (6, 5).
After reflecting across the x-axis:
- The y-coordinate of the first endpoint (0, 5) changes sign: 5 becomes -5.
- The x-coordinate remains the same: 0 remains 0.
- The reflected endpoint is (0, -5).
Similarly,
- The y-coordinate of the second endpoint (6, 5) changes sign: 5 becomes -5.
- The x-coordinate remains the same: 6 remains 6.
- The reflected endpoint is (6, -5).
Therefore, the reflected line segment has endpoints (0, -5) and (6, -5).
The length of the line segment can be found by subtracting the x-coordinates of the endpoints. In this case, the x-coordinates of both endpoints are the same, which means the line segment has a length of 6 - 0 = 6 units.