MATH SOLVE

9 months ago

Q:
# The given line segment has a midpoint at (−1, −2).What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?y = −4x − 4y = −4x − 6y = x – 4y = x – 6

Accepted Solution

A:

we know that

As the midpoint is a point on the perpendicular line, we can solve by eliminating the other equations, like this:

a) Check if the point (-1,-2) is on the line y=-4x-4:

for x=-1

y=-4*(-1)-4--------> y=0

0 is not -2--------> that is not the equation

b) Check if the point (-1,-2) is on the line y = −4x − 6:

for x=-1

y=-4*(-1)-6--------> y=-2

-2 is equal to -2--------> that is the equation

c) Check if the point (-1,-2) is on the line y = x – 4

for x=-1

y=-(-1)-4--------> y=-5

-5 is not -2--------> that is not the equation

d) Check if the point (-1,-2) is on the line y = x – 6

for x=-1

y=-(-1)-6--------> y=-7

-7 is not -2--------> that is not the equation

therefore

the answer is

y = −4x − 6:

As the midpoint is a point on the perpendicular line, we can solve by eliminating the other equations, like this:

a) Check if the point (-1,-2) is on the line y=-4x-4:

for x=-1

y=-4*(-1)-4--------> y=0

0 is not -2--------> that is not the equation

b) Check if the point (-1,-2) is on the line y = −4x − 6:

for x=-1

y=-4*(-1)-6--------> y=-2

-2 is equal to -2--------> that is the equation

c) Check if the point (-1,-2) is on the line y = x – 4

for x=-1

y=-(-1)-4--------> y=-5

-5 is not -2--------> that is not the equation

d) Check if the point (-1,-2) is on the line y = x – 6

for x=-1

y=-(-1)-6--------> y=-7

-7 is not -2--------> that is not the equation

therefore

the answer is

y = −4x − 6: