Find Perpendicular Bisector of Line AB (2,3) & (0,6)

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In summary, To find the cartesian equation for the perpendicular bisector of a line joining points A(2,3) and B(0,6), you must first find the coordinates of the midpoint of the line segment. Then, determine the unit vector parallel to the line segment and the unit vector normal to the line segment's direction. Finally, construct the perpendicular using the midpoint and the normal vector. A bisector is a line that cuts another line into two equal parts.
  • #1
Przybysz
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Find a cartesian equation for the perpendicular bisector of the line joining:
A, (2,3) and B, (0,6).

Haven't come across this before, and really am stuck!

Thanks in advance.
 
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  • #2
Split your problem in several subproblems:
1. What is the coordinates of the midpoint of the line segment?
2. Which unit vector is parallell to the line segment ? (That is, determine the direction vector to the line segment!)
3. Which unit vector is normal to the line segment's direction vector?
4. Construct the perpendicular by using the facts:
a) The perpendicular goes through the midpoint
b) Is parallell to the normal vector
 
Last edited:
  • #3
I'm not so good on maths! What is a bi-sector?
 
  • #4
"bi-sector" bisects the line,i.e. goes through the midpoint of the line.
 
  • #5
"bi" means two, and "sect" means cut. so bisect is "cut in two".
 

What is a perpendicular bisector?

A perpendicular bisector is a line or plane that divides a line segment into two equal parts at a 90-degree angle.

How do you find the perpendicular bisector of a line segment?

To find the perpendicular bisector of a line segment, you will need to find the midpoint of the line segment and then determine the slope of the line. The perpendicular bisector will have a slope that is the negative reciprocal of the original line's slope. You can then use the slope-intercept form to find the equation of the perpendicular bisector.

What is the midpoint formula?

The midpoint formula is used to find the midpoint of a line segment and is calculated by adding the x-coordinates of the endpoints and dividing by 2 for the x-coordinate of the midpoint, and adding the y-coordinates of the endpoints and dividing by 2 for the y-coordinate of the midpoint. In this case, the midpoint would be (1,4.5).

What is the slope-intercept form?

The slope-intercept form is a way to express a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form is useful for finding the equation of a perpendicular bisector because the slope of the perpendicular bisector will be the negative reciprocal of the original line's slope.

How do you know if a line is perpendicular to another line?

A line is perpendicular to another line if their slopes are negative reciprocals of each other. This means that if the slope of one line is m, the slope of the other line will be -1/m. Additionally, the two lines will intersect at a 90-degree angle.

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