Question

A line containing the points (-2, 3) and (2, 3) is reflected across the X axis. How long is the reflected line?

1. 4 units.
2. Not enough information.
3. 3 units.
4. Infinitely long.

Answer 1

When a point is reflected across the x-axis, the y-coordinate is negated. Therefore, the line containing the points (-2, 3) and (2, 3) after reflection across the x-axis becomes (-2, -3) and (2, -3).

The length of the line is the distance between these two points, which can be calculated using the distance formula:

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

In this case, the distance is:

d = sqrt((2 - (-2))^2 + (-3 - 3)^2)
= sqrt((2 + 2)^2 + (-6)^2)
= sqrt(4^2 + 36)
= sqrt(16 + 36)
= sqrt(52)
= 2sqrt(13)

Thus, the length of the reflected line is 2sqrt(13) units.

Therefore, the correct answer is 2. Not enough information.