wikiHow Find the Perpendicular Bisector of Two Points Calculator To find the perpendicular bisector of two points, follow these steps: 1. Determine the midpoint of the line segment that connects the two points. To do this, add the x-coordinates of the two points and divide by 2 to find the x-coordinate of the midpoint, then add the y-coordinates of the two points and divide by 2 to find the y-coordinate of the midpoint. 2. Determine the slope of the line that connects the two points. To do this, subtract the y-coordinate of one point from the y-coordinate of the other point, and divide this by the difference of their x-coordinates. This will give you the slope of the line. 3. Find the negative reciprocal of the slope found in step 2. To do this, flip the slope and change its sign. For example, if the slope found in step 2 is 2/3, the negative reciprocal would be -3/2. 4. Use the midpoint found in step 1 and the negative reciprocal slope found in step 3 to write the equation of the perpendicular bisector in point-slope form. The equation will have the form y - y1 = m(x - x1), where (x1, y1) is the midpoint and m is the negative reciprocal slope. 5. Simplify the equation from step 4 into slope-intercept form (y = mx + b) if desired. The equation of the perpendicular bisector will be the equation of a line that passes through the midpoint of the line segment and is perpendicular to the line segment. Example: Let's say we want to find the perpendicular bisector of the line segment that connects the points (2, 4) and (-2, -2). Here's how we would do it: 1. Find the midpoint: To find the midpoint of the line segment, we add the x-coordinates of the two points and divide by 2, and then add the y-coordinates of the two points and divide by 2: Midpoint = ((2 + (-2))/2, (4 + (-2))/2) = (0, 1) So the midpoint is (0, 1). 2. Find the slope: To find the slope of the line that connects the two points, we use the slope formula: Slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-2 - 2) = -1 So the slope of the line is -1. 3. Find the negative reciprocal of the slope: To find the negative reciprocal of the slope, we flip the slope and change its sign: Negative Reciprocal = -1/-1 = 1 So the negative reciprocal of the slope is 1. 4. Write the equation of the perpendicular bisector in point-slope form: We use the midpoint found in step 1 and the negative reciprocal slope found in step 3 to write the equation of the perpendicular bisector in point-slope form: y - y1 = m(x - x1) y - 1 = 1(x - 0) y = x + 1 So the equation of the perpendicular bisector is y = x + 1. 5. Simplify the equation: We can simplify the equation by writing it in slope-intercept form: y = x + 1 So the equation of the perpendicular bisector is y = x + 1. Page