SOLUTION: Hi. Find the equation of the line parallel to the line y=-8 and passing through the midpoint of the segment joining (-4,2)and (-2,8) thanks. H.C.

Question 179604: Hi.

Find the equation of the line parallel to the line y=-8 and passing through the midpoint of the segment joining (-4,2)and (-2,8)
thanks.
H.C.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's find the midpoint of the segment joining (-4,2)and (-2,8)

To find the midpoint, first we need to find the individual coordinates of the midpoint.

X-Coordinate of the Midpoint:

To find the x-coordinate of the midpoint, simply average the two x-coordinates of the given points by adding them up and dividing that result by 2 like this:

So the x-coordinate of the midpoint is

-----------------------------------------------------

Y-Coordinate of the Midpoint:

To find the y-coordinate of the midpoint, simply average the two y-coordinates of the given points by adding them up and dividing that result by 2 like this:

So the y-coordinate of the midpoint is

So the midpoint of the segment joining the points

and

------------------------------------------------

Now, ANY line parallel to is a horizontal line of the form . Since the parallel line must pass through the midpoint (-3,5) (and the coordinate of this point is ), this means that the parallel line is

Here's a visual confirmation:

Graph of (green) and (blue) through the midpoint (-3,5) of the segment with endpoints (-4,2) and (-2,8)
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