Finding Midpoints

Question

If a line segment A (3x+5,3y) and B(x-1,-y) what are the coordinates of the midpoint of AB

Answer 1

Hi Dhruv from Albertson, NY. Hope you're having a great weekend, getting ready for another school week. I'm here to help you and will get you started on how to answer your question, however, I won't give you the answer, that would be too easy. I'll give you the tools so that when you have another problem like this, you'll be a pro.

Here we go...remember this thing called The Distance Formula?

Hint:  It looks like this:     Distance =   √(x₂−x₁)² + (y₂−y₁)²     

Then since this calculates the distance between two coordinate points, when you divide it by two, you will be able to calculate the midpoint. So your formula will look like this:

           d  =        √(x₂−x₁)² + (y₂−y₁)²    

                                        2

all you need to do is substitute each of the coordinates, which you know into the formula above.

Hint: I'll help you with some of the labeling...

   Your first coordinate is A (3x + 5, 3y)

   Your second coordinate is B (x - 1, -y)

    So now let's label each of your x-coordinates and y-coordinates:

                         x₁ is  3x + 1    and     x₂ is  x - 1

          and          y₁  is  3y         and     y₂ is  -y 

Now all you have to do is substitute the coordinates into the formula.

Hint: If you are able to understand how the distance formula is able to calculate the distance between two coordinate points.

Okay, your turn to work on your problem.

If you get stuck, contact me back on Wyzant.

Answer 2

to find the midpoint, add the x-coordinates (first term in the ordered pair) together and divide by 2 and do the same for the y-coordinates

(4x+4)/2 , 2y/2

(2x+2,y)