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Demonstrate the translation of a line segment of three units to the left and five units down if the endpoints of the line segment are (-2,7) and (0,3).
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If a line segment with endpoints (6,3) and (6,7) is translated three units up and four units to the right, how long is the line segment after the translation?
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A line segment has endpoints (1, 1) and (4, 4). Demonstrating the properties of reflections across the y-axis, what are with the reflected end points?
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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?
Answered by GPT 3.5
To translate a line segment three units to the left and five units down, we need to 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 three units to the left, we subtract 3 from the x-coordinates:
New x-coordinate of (-2) - 3 = -5
New x-coordinate of (0) - 3 = -3

To translate five units down, we subtract 5 from the y-coordinates:
New y-coordinate of 7 - 5 = 2
New y-coordinate of 3 - 5 = -2

Therefore, the translated endpoints are (-5,2) and (-3,-2).
Answered by GPT 3.5
To find the length of the line segment after the translation, we need to calculate the distance between the translated endpoints.

The original endpoints are (6,3) and (6,7).

After translating three units up, the new y-coordinates are:
y-coordinate of 3 + 3 = 6
y-coordinate of 7 + 3 = 10

After translating four units to the right, the new x-coordinates are:
x-coordinate of 6 + 4 = 10
x-coordinate of 6 + 4 = 10

The translated endpoints are (10,6) and (10,10).

To find the length of the line segment, we use the distance formula:

Distance = sqrt( (x2-x1)^2 + (y2-y1)^2 )

Taking (10,6) as (x1,y1) and (10,10) as (x2,y2):

Distance = sqrt( (10-10)^2 + (6-10)^2 )
= sqrt( 0^2 + (-4)^2 )
= sqrt( 0 + 16 )
= sqrt(16)
= 4

Therefore, the length of the line segment after the translation is 4 units.
Answered by GPT 3.5
To reflect a point across the y-axis, we need to negate the x-coordinate while keeping the y-coordinate unchanged.

The original endpoints are (1, 1) and (4, 4).

To reflect the point (1, 1) across the y-axis, we negate the x-coordinate:
The x-coordinate of (1) becomes (-1).
The y-coordinate of (1) remains unchanged.

To reflect the point (4, 4) across the y-axis, we negate the x-coordinate:
The x-coordinate of (4) becomes (-4).
The y-coordinate of (4) remains unchanged.

Therefore, the reflected endpoints across the y-axis are (-1, 1) and (-4, 4).
Answered by GPT 3.5
To reflect a point across the y-axis, we need to negate the x-coordinate while keeping the y-coordinate unchanged.

The original endpoints are (6, -3) and (3, 1).

To reflect the point (6, -3) across the y-axis, we negate the x-coordinate:
The x-coordinate of (6) becomes (-6).
The y-coordinate of (-3) remains unchanged.

To reflect the point (3, 1) across the y-axis, we negate the x-coordinate:
The x-coordinate of (3) becomes (-3).
The y-coordinate of (1) remains unchanged.

Therefore, the new points after reflecting the line across the y-axis are (-6, -3) and (-3, 1).