Find the equation in slope-intercept form of the line that is the perpendicular bisector of the segment between (-3,4) and (3,-8)
Can you help me figure this out?
Thank you!
slope is (-8-4)/(3 - -3) = -2
Now plug in the point-slope form:
y-4 = -2(x+3)
Now it's easy, right?
y = 1/2x - 2
Is that right?
Yes, I can help you with that!
To find the equation of the perpendicular bisector, we need to follow a few steps:
Step 1: Find the midpoint of the segment
Step 2: Find the slope of the segment
Step 3: Find the negative reciprocal of the slope
Step 4: Use the midpoint and the negative reciprocal slope to find the equation in slope-intercept form
Let's go through each step:
Step 1: Finding the midpoint
The midpoint of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using the given points (-3, 4) and (3, -8), we can calculate the midpoint:
Midpoint = ((-3 + 3) / 2, (4 + -8) / 2)
= (0/2, -4/2)
= (0, -2)
So, the midpoint of the segment is (0, -2).
Step 2: Finding the slope of the segment
The slope of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
Slope = (y2 - y1) / (x2 - x1)
Using the given points (-3, 4) and (3, -8), we can calculate the slope:
Slope = (-8 - 4) / (3 - (-3))
= (-12) / 6
= -2
So, the slope of the segment is -2.
Step 3: Finding the negative reciprocal of the slope
The negative reciprocal of a number x is given by:
Negative Reciprocal = -1 / x
In our case, the negative reciprocal of -2 is:
Negative Reciprocal = -1 / (-2)
= 1/2
So, the negative reciprocal of the slope -2 is 1/2.
Step 4: Finding the equation in slope-intercept form
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
We already have the slope (1/2) and the midpoint (0, -2). To find the y-intercept, we can substitute the values of x and y from the midpoint into the equation and solve for b.
Using the equation y = mx + b:
-2 = (1/2)(0) + b
-2 = 0 + b
b = -2
So, the y-intercept is -2.
Putting it all together, the equation of the line that is the perpendicular bisector of the segment between (-3, 4) and (3, -8) in slope-intercept form is:
y = (1/2)x - 2
I hope this explanation helps you understand how to find the equation of the perpendicular bisector! Let me know if you have any further questions.