A line contains the points (−4, 2) and (−4, 6) . The line is translated 3 units to the right and 2 units down. What are the new points on the translated line?

Answer 1

To translate a point in the coordinate plane, we need to add or subtract values from the x and y coordinates. Since we want to translate the line 3 units to the right and 2 units down, we add 3 to the x coordinate and subtract 2 from the y coordinate.

For the first point (-4,2), we add 3 to -4 and subtract 2 from 2:
x-coordinate: -4 + 3 = -1
y-coordinate: 2 - 2 = 0

So the new point is (-1,0).

For the second point (-4,6), we add 3 to -4 and subtract 2 from the y coordinate:
x-coordinate: -4 + 3 = -1
y-coordinate: 6 - 2 =4

So the new point is (-1,4).

Therefore, the new points on the translated line are (-1,0) and (-1,4).

Answer 2

A line segment is translated 3 units down and 1 unit to the left. One of the endpoints after the translation is (5, 8) . What was this point before the translation?

Answer 3

To find the original point before the translation, we need to reverse the translation by adding 3 to the y-coordinate and subtracting 1 from the x-coordinate.

For the point (5,8), we add 3 to 8 and subtract 1 from 5:
x-coordinate: 5 - 1 = 4
y-coordinate: 8 + 3 = 11

So the original point before the translation is (4,11).

Answer 4

the answer is wrong

Answer 5

Apologies for the mistake. Let's correct it.

To find the original point before the translation, we need to reverse the translation by adding 3 to the y-coordinate and subtracting 1 from the x-coordinate.

For the point (5,8), we add 3 to 8 and subtract 1 from 5:
x-coordinate: 5 - 1 = 4
y-coordinate: 8 - 3 = 5

So the original point before the translation is (4,5).

Answer 6

Reflect the point (13, 8) across the y -axis. What is the result?

Answer 7

To reflect a point across the y-axis, we simply change the sign of the x-coordinate while keeping the y-coordinate the same.

For the point (13,8), we change the sign of the x-coordinate:
x-coordinate: -13
y-coordinate: 8

So the result of reflecting the point (13,8) across the y-axis is (-13,8).

Answer 8

Reflect the endpoint of a line segment (−5, 10) across the x -axis. What is the result?

Answer 9

To reflect a point across the x-axis, we simply change the sign of the y-coordinate while keeping the x-coordinate the same.

For the endpoint of the line segment (-5,10), we change the sign of the y-coordinate:
x-coordinate: -5
y-coordinate: -10

So the result of reflecting the endpoint (-5,10) across the x-axis is (-5,-10).