The equation in slope-intercept form of the line that is the perpendicular bisector of the segment between (-3, 2) and (3, -8) is:
[tex]y=\frac{3}{5}x-3[/tex]
Step-by-step explanation:
As the required line is perpendicular bisector of the given line segment, it will pass through the mid-point of the given line segment.
(x1,y1) = (-3,2)
(x2,y2) = (3,-8)
so,
[tex]Mid-point = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\=(\frac{-3+3}{2}, \frac{2-8}{2})\\=(\frac{0}{2},\frac{-6}{2})\\=(0, -3)[/tex]
We also have to find the slope of the required line
Let m1 be the slope of given line and m2 be the slope of required line
so,
[tex]m_1 = \frac{y_2-y_1}{x_2-x_1}\\=\frac{-8-2}{3+3}\\=\frac{-10}{6}\\=-\frac{5}{3}[/tex]
The product of slopes of two perpendicular lines is -1, So
[tex]-\frac{5}{3}*m_2=-1\\m_2=-1 * -\frac{3}{5}\\m_2=\frac{3}{5}[/tex]
Slope-intercept form is:
[tex]y=m_2x+b[/tex]
Putting the value of m2
[tex]y=\frac{3}{5}x+b[/tex]
As the line passes through (0,-3)
[tex]-3=\frac{3}{5}*0 + b\\-3=b[/tex]
So.,
The equation in slope-intercept form of the line that is the perpendicular bisector of the segment between (-3, 2) and (3, -8) is:
[tex]y=\frac{3}{5}x-3[/tex]
Keywords: Slope-intercept form, Slope
Learn more about equation of line at:
- brainly.com/question/4021035
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