Find an equation for the perpendicular bisector of the line segment whose endpoints (5, -3) and (-7, -7).
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Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the midpoint of the line segment

When two lines bisect each other, they intersect at the middle of each line, or the midpoint.

Plug in the endpoints (5, -3) and (-7, -7)

Therefore, the midpoint of the line segment is (-1,-5).

2) Determine the slope of the line segment

Recall that the slopes of perpendicular lines are negative reciprocals. Doing this will help us determine the slope of the perpendicular bisector.

Slope = where the given points are and

Plug in the endpoints (5, -3) and (-7, -7)

Therefore, the slope of the line segment is . The negative reciprocal of is -3, so the slope of the perpendicular is -3. Plug this into :

3) Determine the y-intercept of the perpendicular bisector (b)

Recall that the midpoint of the line segment is is (-1,-5), and that the perpendicular bisector passes through this point. Plug this point into and solve for b:

Subtract 3 from both sides

Therefore, the y-intercept of the line is -8. Plug this back into :

I hope this helps!

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is