To translate a line segment 3 units to the left and 5 units down, we need to subtract 3 from the x-coordinates and subtract 5 from the y-coordinates of the endpoints.
Starting with the first endpoint (-2, 7), we subtract 3 from the x-coordinate and subtract 5 from the y-coordinate:
New x-coordinate: -2 - 3 = -5
New y-coordinate: 7 - 5 = 2
So the translated first endpoint is (-5, 2).
Similarly, for the second endpoint (0, 3), we subtract 3 from the x-coordinate and subtract 5 from the y-coordinate:
New x-coordinate: 0 - 3 = -3
New y-coordinate: 3 - 5 = -2
So the translated second endpoint is (-3, -2).
Therefore, the line segment is translated to a new line segment with endpoints (-5, 2) and (-3, -2).
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) .(1 point)
Responses
11 answers
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?(1 point)
To translate a line segment 3 units up and 4 units to the right, we need to add 3 to the y-coordinates and add 4 to the x-coordinates of the endpoints.
Starting with the first endpoint (6, 3), we add 3 to the y-coordinate and add 4 to the x-coordinate:
New x-coordinate: 6 + 4 = 10
New y-coordinate: 3 + 3 = 6
So the translated first endpoint is (10, 6).
Similarly, for the second endpoint (6, 7), we add 3 to the y-coordinate and add 4 to the x-coordinate:
New x-coordinate: 6 + 4 = 10
New y-coordinate: 7 + 3 = 10
So the translated second endpoint is (10, 10).
Therefore, the line segment is translated to a new line segment with endpoints (10, 6) and (10, 10).
To calculate the length of the line segment, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, using the coordinates of the translated endpoints:
d = √((10 - 10)^2 + (10 - 6)^2)
= √(0 + 16)
= √16
= 4
Therefore, the length of the line segment after the translation is 4 units.
Starting with the first endpoint (6, 3), we add 3 to the y-coordinate and add 4 to the x-coordinate:
New x-coordinate: 6 + 4 = 10
New y-coordinate: 3 + 3 = 6
So the translated first endpoint is (10, 6).
Similarly, for the second endpoint (6, 7), we add 3 to the y-coordinate and add 4 to the x-coordinate:
New x-coordinate: 6 + 4 = 10
New y-coordinate: 7 + 3 = 10
So the translated second endpoint is (10, 10).
Therefore, the line segment is translated to a new line segment with endpoints (10, 6) and (10, 10).
To calculate the length of the line segment, we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, using the coordinates of the translated endpoints:
d = √((10 - 10)^2 + (10 - 6)^2)
= √(0 + 16)
= √16
= 4
Therefore, the length of the line segment after the translation is 4 units.
A line segment has endpoints (1, 1) and (4, 4) . Demonstrating the properties of reflections across the y -axis, what are the reflected endpoints?(1 point)
To reflect a point across the y-axis, we negate the x-coordinate while keeping the y-coordinate the same.
Starting with the first endpoint (1, 1), we negate the x-coordinate:
New x-coordinate: -1
Y-coordinate remains unchanged: 1
So the reflected first endpoint is (-1, 1).
Similarly, for the second endpoint (4, 4), we negate the x-coordinate:
New x-coordinate: -4
Y-coordinate remains unchanged: 4
So the reflected second endpoint is (-4, 4).
Therefore, the reflected endpoints after the reflection across the y-axis are (-1, 1) and (-4, 4).
Starting with the first endpoint (1, 1), we negate the x-coordinate:
New x-coordinate: -1
Y-coordinate remains unchanged: 1
So the reflected first endpoint is (-1, 1).
Similarly, for the second endpoint (4, 4), we negate the x-coordinate:
New x-coordinate: -4
Y-coordinate remains unchanged: 4
So the reflected second endpoint is (-4, 4).
Therefore, the reflected endpoints after the reflection across the y-axis are (-1, 1) and (-4, 4).
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?(1 point)
To reflect a point across the y-axis, we need to negate the x-coordinate while keeping the y-coordinate the same.
Starting with the first point (6, -3), we negate the x-coordinate:
New x-coordinate: -6
Y-coordinate remains the same: -3
So the reflected first point is (-6, -3).
Similarly, for the second point (3, 1), we negate the x-coordinate:
New x-coordinate: -3
Y-coordinate remains the same: 1
So the reflected second point is (-3, 1).
Therefore, the two new points after reflecting the line across the y-axis are (-6, -3) and (-3, 1).
Starting with the first point (6, -3), we negate the x-coordinate:
New x-coordinate: -6
Y-coordinate remains the same: -3
So the reflected first point is (-6, -3).
Similarly, for the second point (3, 1), we negate the x-coordinate:
New x-coordinate: -3
Y-coordinate remains the same: 1
So the reflected second point is (-3, 1).
Therefore, the two new points after reflecting the line 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?(1 point)
Responses
Responses
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.
Starting with the first endpoint (0, 5), the y-coordinate becomes negative:
New y-coordinate: -5
X-coordinate remains the same: 0
So the reflected first endpoint is (0, -5).
Similarly, for the second endpoint (6, 5), the y-coordinate becomes negative:
New y-coordinate: -5
X-coordinate remains the same: 6
So the reflected second endpoint is (6, -5).
To find the length of the line segment after the reflection, we can calculate the horizontal distance between the x-coordinates of the two endpoints:
Length = |x2 - x1|
Length = |6 - 0|
Length = 6
Therefore, the length of the line segment after being reflected across the x-axis is 6 units.
Starting with the first endpoint (0, 5), the y-coordinate becomes negative:
New y-coordinate: -5
X-coordinate remains the same: 0
So the reflected first endpoint is (0, -5).
Similarly, for the second endpoint (6, 5), the y-coordinate becomes negative:
New y-coordinate: -5
X-coordinate remains the same: 6
So the reflected second endpoint is (6, -5).
To find the length of the line segment after the reflection, we can calculate the horizontal distance between the x-coordinates of the two endpoints:
Length = |x2 - x1|
Length = |6 - 0|
Length = 6
Therefore, the length of the line segment after being reflected across the x-axis is 6 units.
1. (−5, 2) and (−3,−2)
2. 4 units
3. (-1, 1) and (-4, 4)
4. (-6, -3) and (-3, 1)
5. 6 units
2. 4 units
3. (-1, 1) and (-4, 4)
4. (-6, -3) and (-3, 1)
5. 6 units
Your responses are correct:
1. The reflected endpoints of (-5, 2) and (-3, -2) are given by negating the x-coordinates, resulting in (5, 2) and (3, -2).
2. After reflecting the line segment across the y-axis, the length remains the same at 4 units.
3. The reflected endpoints of (1, 1) and (4, 4) across the y-axis are (-1, 1) and (-4, 4).
4. The reflected endpoints of (6, -3) and (3, 1) across the y-axis are (-6, -3) and (-3, 1).
5. After reflecting the line segment across the x-axis, the length of 6 units remains the same.
1. The reflected endpoints of (-5, 2) and (-3, -2) are given by negating the x-coordinates, resulting in (5, 2) and (3, -2).
2. After reflecting the line segment across the y-axis, the length remains the same at 4 units.
3. The reflected endpoints of (1, 1) and (4, 4) across the y-axis are (-1, 1) and (-4, 4).
4. The reflected endpoints of (6, -3) and (3, 1) across the y-axis are (-6, -3) and (-3, 1).
5. After reflecting the line segment across the x-axis, the length of 6 units remains the same.
1 answer