Question

A line segment has endpoints (1,1) and (4,4). Demonstrating the properties of reflections across the y-axis, what are the reflected endpoints?

(-1,1) and (-4,4)

(-1,-1) and (-4,-4)

(-1,1) and (4,4)

(1,-1) and (4,-4)

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

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

When we reflect (1,1), the x-coordinate changes from 1 to -1 while the y-coordinate remains the same. Therefore, the reflected endpoint is (-1,1).

Similarly, when we reflect (4,4), the x-coordinate changes from 4 to -4 while the y-coordinate remains the same. Therefore, the reflected endpoint is (-4,4).

So, the correct answer is (-1,1) and (-4,4).

Answer 2

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?

(-6,-3) and (-3,1)

(6,3) and (3,-1)

(-6,3) and (-3,-1)

(-6,-3) and (3,1)

Answer 3

[AI-generated answer — Bot GPT 3.5]

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

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

When we reflect (6,-3), the x-coordinate changes from 6 to -6 while the y-coordinate remains the same. Therefore, the reflected point is (-6,-3).

Similarly, when we reflect (3,1), the x-coordinate changes from 3 to -3 while the y-coordinate remains the same. Therefore, the reflected point is (-3,1).

So, the correct answer is (-6,-3) and (-3,1).

Answer 4

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?

11 units

1 units

6 units

5 units

Answer 5

[AI-generated answer — Bot GPT 3.5]

When a line segment is reflected across the x-axis, the y-coordinates change sign while the x-coordinates remain the same.

The original line segment has endpoints (0,5) and (6,5).

When we reflect these points across the x-axis, the y-coordinate of (0,5) changes from 5 to -5 while the x-coordinate remains the same. Similarly, the y-coordinate of (6,5) changes from 5 to -5 while the x-coordinate remains the same.

The reflected line segment has endpoints (0,-5) and (6,-5).

To find the length of the line segment, we subtract the x-coordinates of the endpoints. In this case, the x-coordinates are the same, so the length of the line segment remains the same.

Therefore, the length of the reflected line segment is 6 units.