MIDPOINT FORMULA!!!!! ?

Question

find the midpoint of the line segment joining the points (7, 4) and (-8, 7)

i worked it out and i got (15/2, -3/2) is this the answer...

thank you for the help

ps: ive noticed that people that post hw problems jst post the problems but they only want the answer without doing any work..in my case i try to do the problem and if i dont think its correct at least i write the answer i got =)

thanks again!!!

Answer 1

I'd like to encourage you not to consider the formula first!  Before you begin, try to think about the points on a graph, and make a rough guess about what area the midpoint should be in.  As an added benefit, thinking about the question conceptually first will allow you to "check" your answer after applying the formula, to make sure it makes sense.

First, consider just the horizontal position (x-coordinate) of each point.  The first point has an x-coordinate of 7, and the other -8.  This means one point is 7 units to the right of the origin, and the other is 8 units to the left of the origin.  Thinking of it this way, it should be clear that the midpoint of the two should have an x-coordinate near the origin (slightly left of the origin, although that might be less obvious right now).

Then, consider then vertical position (y-coordinate) of each point.  The first point has a y-value of 4, and the second has a y-value of 7.  So, the midpoint must have a y-value between 4 and 7.

Now, apply the formula -- which is to add the two x-values, divide by 2, and do the same to do the y-values.  In this case...

Midpoint's x-coordinate: (7 + (-8)) / 2 = -1 / 2 = - (1/2)

Midpoint's y-coordinate: (4 + 7) / 2 = 11/2

So the midpoint is at (-1/2, 11/2).  Checking what we thought about conceptually, it's consistent: -1/2 is slightly left of the origin, and 11/2 is between 4 and 7.

I realize the conceptual part may just seem like an extra step right now, but trust me, what you learn in math doesn't go away!  It'll help you later to get a very firm grasp on it now, and be able to check your own work!

Good luck!

Answer 2

x1+x2 / 2

y1+y2 / 2

i got ( -0.5, 5.5)