Question

A line segment has endpoints at (4.-6) and (0,2).

Answer 1

Answer:

see explanation

Step-by-step explanation:

Calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2)

m = $\frac{2+6}{0-4}$ = $\frac{8}{-4}$ = - 2

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Find the midpoint using the midpoint formula

M =( $\frac{x_{1}+x_{2} }{2}$ , $\frac{y_{1}+y_{2} }{2}$ )

    = $\frac{4+0}{2}$ , $\frac{-6+2}{2}$ ) = (2, - 2 )

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Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-2}$ = $\frac{1}{2}$

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The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = $\frac{1}{2}$ , thus

y = $\frac{1}{2}$ x + c ← is the partial equation

To find c substitute (2, - 2) into the partial equation

- 2 = 1 + c ⇒ c = - 2 - 1 = - 3

y = $\frac{1}{2}$ x - 3 ← equation of perpendicular bisector

Answer 2

Answer:

• -2
• (2, -2)
• 1/2
• y= 1/2x - 3

Step-by-step explanation:

Points given: (4, -6) and (0, 2)

Slope intercept form of the line going through the given pints:

y= mx+b

• m= (y2-y1)/(x2-x1)= (2+6)/(0-4)= -2  slope is -2

y= -2x+b ⇒ -6= -2*4+b ⇒ b= 8-6= 2 ⇒ y= -2x+2

• Mid point= (x1+x2)/2, (y1+y2)/2= (4+0)/2, (-6+2)/2= (2, -2)

The slope of the perpendicular bisector is the negative reciprocal of the line segment which it is dividing:

• m'= -1/m= -1/-2= 1/2

Equation of perpendicular bisector:

• y= 1/2x+b

It passes through the mid point: (2, -2), so

• b= y - 1/2x= -2 - 1/2*2= -2 -1= -3

So the equation of perpendicular line:

• y= 1/2x - 3