write and equation on point sloop form for the perpendicular bisector of the segment with endpoints A(-3,-3) and B(5,6)

Should this be Write an equation in point slope form...?

find the slope between A,B

Then, take the negative reciprocal of that slope, this will be she slope of the perpendicular.

Now, find the median point where the "bisector" intersects.

x= (-3+5)/2
y= (-3=6)/2

then, y= mx+b
you found m the slope of the perpendicular, and you know x,y, so find b.

To write the equation of the perpendicular bisector in point-slope form, we need two pieces of information: the midpoint and the slope.

Step 1: Find the midpoint of the segment.
The midpoint formula is given by:
Midpoint (M) = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Given point A(-3, -3) and point B(5, 6), we can find the midpoint as follows:
Midpoint (M) = ((-3 + 5)/2, (-3 + 6)/2)
Midpoint (M) = (2/2, 3/2)
Midpoint (M) = (1, 3/2)
Therefore, the midpoint of the segment AB is M(1, 3/2).

Step 2: Find the slope of the segment AB.
Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Given point A(-3, -3) and point B(5, 6), we can find the slope as follows:
Slope (m) = (6 - (-3))/(5 - (-3))
Slope (m) = 9/8
Hence, the slope of the segment AB is 9/8.

Step 3: Find the negative reciprocal of the slope obtained in step 2.
The negative reciprocal of a number 'a' is -1/a.
Hence, the negative reciprocal of 9/8 is -8/9.

Step 4: Write the equation using the point-slope form.
The equation of the perpendicular bisector passing through the midpoint (1, 3/2) with a slope of -8/9 can be written as:
y - y₁ = m(x - x₁)
y - 3/2 = -8/9(x - 1)

This is the equation of the perpendicular bisector in point-slope form for the segment with endpoints A(-3, -3) and B(5, 6).