Points: (-2, 2) and (6, 4)
Midpoint: (2, 3)
Slope: 1/4
Perpendicular slope: -4
Perpendicular bisector equation: y-3 = -4(x-2) => y = -4x+11
Perpendicular Bisector
I believe this is called the perpendicular bisector.
It's called a perpendicular bisector of the line segment.
perpendicular bisector
The perpendicular bisector of a line segment AB is the straight line perpendicular to AB through the midpoint of AB.
Points: (-1, -6) and (5, -8) Midpoint: (2, -7) Perpendicular slope: 3 Perpendicular bisector equation: y = 3x -13
perpendicular bisector
Perpendicular Bisector
A segment that intersects the midpoint of another segment and is perpendicular to it is known as the "perpendicular bisector." This line segment divides the original segment into two equal parts at the midpoint and forms right angles (90 degrees) with the original segment. The perpendicular bisector has important properties in geometry, particularly in triangle constructions and circumcircles.
A midpoint is a point. It's the point exactly halfway between the endsof a line segment.A perpendicular bisector is a line. It's the line that passes through themidpoint of the segment, and is perpendicular to the segment.
To find the perpendicular bisector of a line segment, first, determine the midpoint of the segment by averaging the x-coordinates and y-coordinates of the endpoints. Next, calculate the slope of the line segment and find the negative reciprocal of that slope to get the slope of the perpendicular bisector. Then, use the midpoint and the new slope to write the equation of the perpendicular bisector in point-slope form. Finally, you can convert it to slope-intercept form if needed.
Endpoints: (-2, 4) and (6, 8) Slope: 1/2 Perpendicular slope: -2 Midpoint: (2, 6) Perpendicular bisector equation: y = -2x+10