A perpendicular bisector is a segment which is perpendicular to another segment, and specifically goes through the midpoint of the segment. Find the equation of the perpendicular bisector of in slope intercept form, given A(3,6) and B(3, 10) .
im not sure
To find the equation of the perpendicular bisector of the line segment AB, we need to follow these steps.
Step 1: Find the midpoint of AB.
Step 2: Determine the slope of AB.
Step 3: Find the negative reciprocal of the slope of AB to get the slope of the perpendicular bisector.
Step 4: Use the midpoint and slope of the perpendicular bisector to write the equation in slope-intercept form.
Let's go through these steps:
Step 1: Find the midpoint of AB.
The midpoint formula is ( (𝑥₁ + 𝑥₂)/2, (𝑦₁ + 𝑦₂)/2 ).
Substituting the given coordinates, we have:
Midpoint = ( (3 + 3)/2, (6 + 10)/2 )
= ( 6/2, 16/2 )
= ( 3, 8 )
Step 2: Determine the slope of AB.
The slope formula is 𝑚 = (𝑦₂ - 𝑦₁)/(𝑥₂ - 𝑥₁)
Substituting the given coordinates, we have:
Slope of AB = (10 - 6)/(3 - 3)
= (4/0) (Note that the denominator is zero, which means the line AB is vertical. The slope of a vertical line is undefined.)
Since we have an undefined slope, we cannot proceed further using Step 3. Instead, we will use a different approach to find the equation of the perpendicular bisector.
Step 2 alternative approach: Determine the equation of the vertical line passing through the midpoint.
Since a vertical line passing through the point (x, y) has an equation of x = x_coordinate, we can write the equation of the vertical line passing through the midpoint (3, 8) as x = 3.
Hence, the equation of the vertical line passing through the midpoint is x = 3.
Therefore, the perpendicular bisector of AB is the vertical line x = 3.