Respuesta :
Answer:
y = -x - 8
Step-by-step explanation:
Midpoint of the line:
x = (x1 + x2)/2 = (-8 + -4)/2 = -12/2 = -6
y = (y1 + y2)/2 = (-5 + 1)/2 = -4/2 = -2
so midpoint is (-6,-2)
Slope of the line: Slope m = (y2-y1)/(x2-x1)
m = (-1 - -5)/(-4 - -8) = (-1 + 5)/(-4 + 8) = 4/4 = 1
Perpendicular lines have slopes that are negative reciprocals of one another
so slope of the perpendicular line is -1/1 is -1
y = mx + b
y = -x + b
Using (-6,-2)
-2 = -(-6) + b
-2 = 6 + b
b = -8
so y = -x - 8
Answer:
[tex]y=\frac{3}{2}x-3[/tex]
Step-by-step explanation:
Step 1: Perpendicular bisector
To find the perpendicular bisector of the segment, apply the midpoint formula:
[tex]\bigg(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\bigg)[/tex]
Points: {(-8, -5, (-4, 1)}
x₁ = -8 first x value
x₂ = -4 second x value
y₁ = -5 first y value
y₂ = 1 second y value
Plug the points into the formula:
[tex]\bigg(\frac{-8+(-4)}{2}, \frac{-5+1}{2}\bigg)[/tex]
Solve:
[tex]\bigg(\frac{-8+(-4)}{2}, \frac{-5+1}{2}\bigg)[/tex]
[tex]=\bigg(\frac{-12}{2}, \frac{-4}{2}\bigg)[/tex]
[tex]=(-6,-2)[/tex]
The midpoint is (-6, -2).
Step 2: Slope
To find the slope (m), apply the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
(point location is the same as previous step)
Plug the points into the formula; then solve:
[tex]\frac{1-(-5)}{-4(-8)}[/tex]
[tex]=\frac{6}{4}[/tex]
[tex]m=\frac{3}{2}[/tex]
The slope is 3/2
Step 3: Solving for b
[tex]y = mx+b[/tex]
[tex]-6=\frac{3}{2}(-2)+b[/tex]
[tex]\frac{3}{2}\left(-2\right)+b=-6[/tex]
[tex]-\frac{3}{2}\cdot \:2+b=-6[/tex]
[tex]-3+b=-6[/tex]
[tex]-3+b+3=-6+3[/tex]
[tex]b=-3[/tex]
Therefore, the equation is [tex]\bold{-6=\frac{3}{2}(-2)-3}[/tex]
