The "perpendicular bisector" of the line segment \overline{AB}(The backslash then over line with the {AB} means that there's a line over AB) is the line that passes through the midpoint of \overline{AB} and is perpendicular to \overline{AB}.
yeah, what about it?
"bisect" means it divides into two equal parts.
To find the perpendicular bisector of a line segment AB, you need to follow these steps:
1. Determine the midpoint of line segment AB:
- To find the midpoint, you can use the midpoint formula:
- The x-coordinate of the midpoint (Mx) is found by averaging the x-coordinates of A and B: Mx = (Ax + Bx) / 2
- The y-coordinate of the midpoint (My) is found by averaging the y-coordinates of A and B: My = (Ay + By) / 2
2. Find the slope of line segment AB:
- The slope (m) of line segment AB is given by the formula: m = (By - Ay) / (Bx - Ax)
3. Determine the negative reciprocal of the slope:
- The negative reciprocal of the slope is obtained by taking the negative value of the reciprocal of the slope: -1/m
4. Use the midpoint and the negative reciprocal slope to find the equation of the perpendicular bisector:
- The equation of a line, in point-slope form, is given by: y - y1 = m(x - x1), where (x1, y1) is any point on the line and m is the slope of the line.
- Substitute the values of the midpoint (Mx, My) and the negative reciprocal of the slope (-1/m) into the equation to find the equation of the perpendicular bisector.
By following these steps, you can determine the equation of the perpendicular bisector of line segment AB.