The line segment EF is presented on a coordinate grid, with endpoints at (-3, 2) and (-1, 2). When the line segment is reflected across the x-axis, it forms E'F'. Which statement accurately describes E'F'? - E'F' and EF have the same length. - E'F' is half the length of EF. - E'F' is more than twice the length of EF. - E'F' and EF are perpendicular.

E'F' and EF have the same length.

When a line segment is reflected across the x-axis, each point on the line segment is reflected as well. The x-coordinates remain the same, while the y-coordinates are multiplied by -1 (i.e., the sign of the y-coordinates is changed). Since reflection is an isometry (distance-preserving transformation), the distances between points, and consequently the lengths of line segments, remain the same before and after the reflection.

Given the endpoints of EF are at (-3, 2) and (-1, 2), we can find the corresponding points for E'F' by changing the sign of the y-coordinates. This gives us points E' at (-3, -2) and F' at (-1, -2). This line segment E'F' is directly below EF on the coordinate grid and both line segments are horizontal, parallel to the x-axis. Since the original and reflected line segments have not changed in length, the accurate statement is that E'F' and EF have the same length.

Extra: Reflection across the x-axis does not alter the distance between two points along the horizontal direction, which means that the length of the segment remains the same. The line segment EF is horizontal and so is its reflection E'F', because the y-coordinates are the same for the end points of both EF and E'F' and only the sign is different. Both line segments are parallel to the x-axis, and their lengths can be calculated using the distance formula for two points (A(x1,y1) and B(x2,y2)) given by \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2} \). However, since EF and E'F' are horizontal, we can also find their lengths by simply calculating the absolute difference between the x-coordinates of the endpoints. In essence, reflecting a line segment across the x-axis, y-axis, or any line parallel to the x or y-axis, will always result in a line segment of equal length to the original. This is because reflections are a type of rigid transformation, which means they do not change the size or shape of geometric figures.