Find te equation in slope-intercept form of the line that is the perpendicular bisector of the segment between (-3,4) and (3,-8).
find the midpoint ((-3+3)/2, (4-8)/2)
I think that is 0,-2 check it.
now find the slope: changey/changex
slope= 4+8 / -3-3= 12/-6=-2
perpendicular slope= 1/2 (negative reciprocal).
So the question now is find the equation of the line with slope 1/2, and has the point 0,-2 in it
y=mx+b
put in m, y, and x, solve for b, and you have the line
y=mx + b
To find the equation in slope-intercept form of the line that is the perpendicular bisector of the segment between (-3, 4) and (3, -8), we'll need to follow these steps:
Step 1: Find the midpoint of the segment
The midpoint of the segment is the average of the x-coordinates and the average of the y-coordinates. So we have:
Midpoint(x, y) = ((-3 + 3)/2, (4 + (-8))/2) = (0, -2)
Step 2: Find the slope of the segment
The slope of the segment can be found using the formula:
Slope = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (-3, 4) and (3, -8), the slope is:
Slope = (-8 - 4) / (3 - (-3)) = (-12) / 6 = -2
Step 3: Find the negative reciprocal of the slope
To find the slope of the perpendicular bisector, we need to find the negative reciprocal of the slope found in step 2. The negative reciprocal of -2 is 1/2.
Step 4: Use the midpoint and the perpendicular slope to find the equation
Now that we have the midpoint (0, -2) and the slope 1/2, we can use the slope-intercept form of a line:
y = mx + b
Substituting the values, we get:
-2 = (1/2)(0) + b
-2 = 0 + b
b = -2
Therefore, the equation in slope-intercept form of the line that is the perpendicular bisector of the segment between (-3, 4) and (3, -8) is:
y = (1/2)x - 2