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 − 4 y = −4x − 6 y = x – 4 y = x – 6

Option 2 is correct. y=-4x-6

Explanation:

We are given a point (-1,-2). This is mid point of given segement.

Let AB be asegement with mid point M(-1,-2) as shown in figure.

We need to find the equation line in slope intercept form which is perpendicular bisector of segement AB.

As we know perpendicular bisector line always passing through the mid point of segement.

So, we will check given point (-1,-2) with all option to satisfy.

Option 1) y=-4x-4

Put x=-1 and y=-2 into equation and we get

Does't satisfy this equation. This won't be a solution.

Option 2) y=-4x-6

Put x=-1 and y=-2 into equation and we get

(-1,-2) satisfy given equation y=-4x-6. This would be solution.

Option 3) y=x-4

Put x=-1 and y=-2 into equation and we get

Does't satisfy this equation. This won't be a solution.

Option 4) y=x-6

Put x=-1 and y=-2 into equation and we get

Does't satisfy this equation. This won't be a solution.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.