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 to the left by 3 units and down by 5 units, we subtract 3 from the x-coordinates and subtract 5 from the y-coordinates of the endpoints.
The original endpoints are (-2, 7) and (0, 3).
To translate 3 units to the left:
New x-coordinate of (-2) - 3 = -5
New x-coordinate of (0) - 3 = -3
To translate 5 units down:
New y-coordinate of 7 - 5 = 2
New y-coordinate of 3 - 5 = -2
Therefore, the translated endpoints are (-5, 2) and (-3, -2).
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 4 to the x-coordinates and add 3 to the y-coordinates of the endpoints.
The original endpoints are (6, 3) and (6, 7).
To translate 4 units to the right:
New x-coordinate of 6 + 4 = 10
To translate 3 units up:
New y-coordinate of 3 + 3 = 6
New y-coordinate of 7 + 3 = 10
Therefore, the translated endpoints are (10, 6) and (10, 10).
To find the length of the line segment after the translation, we use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
d = √[(10 - 10)^2 + (10 - 6)^2]
d = √[0^2 + 4^2]
d = √[0 + 16]
d = √16
d = 4
The line segment has a length of 4 units after the translation.
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 negate the x-coordinate. Thus, to reflect the line segment with endpoints (1, 1) and (4, 4) across the y-axis, we negate the x-coordinates of the endpoints.
The original endpoints are (1, 1) and (4, 4).
To reflect across the y-axis:
New x-coordinate of 1: -1
New x-coordinate of 4: -4
Therefore, the reflected endpoints 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?
To reflect a point across the y-axis, we negate the x-coordinate. Thus, to reflect the line with endpoints (6,−3) and (3, 1) across the y-axis, we negate the x-coordinates of the endpoints.
The original endpoints are (6,−3) and (3, 1).
To reflect across the y-axis:
New x-coordinate of 6: -6
New x-coordinate of 3: -3
Therefore, the reflected endpoints 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 change their signs while the x-coordinates remain the same.
The original endpoints are (0, 5) and (6, 5). After reflecting across the x-axis, the y-coordinates become negative.
The reflected endpoints are (0, -5) and (6, -5).
To find the length of the line segment after the reflection, we use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((6 - 0)^2 + (-5 - (-5))^2)
d = √(6^2 + 0^2)
d = √(36 + 0)
d = √36
d = 6
Therefore, the length of the line segment after reflecting across the x-axis remains 6 units.