Question

How do you find the midpoint of (5,-2), (3,-6)?

Answer 1

See the entire solution process below:

Explanation:

The formula to find the mid-point of a line segment give the two end points is:

`M = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)`

Where `M` is the midpoint and the given points are:

`(color(red)((x_1, y_1)))` and `(color(blue)((x_2, y_2)))`

Substituting the values from the points in the problem gives:

`M = ((color(red)(5) + color(blue)(3))/2 , (color(red)(-2) + color(blue)(-6))/2)`

`M = (8/2 , -8/2)`

`M = (4, -4)`

Answer 2

`(4,2)`

Explanation:

The midpoint of a segment with endpoints:

`A = (x_1, y_1) and B = (x_2, y_2)` has coordinates :

`[(x_1 + x_2) /2 , (y_1 + y_2)/2]`

So in this case the midpoint is:

`[(5+3)/2,(-2-(-6))/2]` => simplify:

`[8/2,(-2+6)/2]`

`(4,2)`

Answer 3

The midpoint of (5 , -2), (3 , -6) is (4 , -4)

Explanation:

The midpoint formula is `((x_1+x_2)/2 , (y_1+y_2)/2)`

For your points

`x_1` = 5 because your first point on "x" is 5 from (5,-2)

`x_2` = 3 because your second point on "x" is 3 from (3,-6)

`y_1` = -2 because your first point on "y" is -2 from (5,-2)

`y_2` = -6 because your second point on "y" is -6 from (3,-6)

From here all you need to do is substitute values.

`(((5)+(3))/2 , ((-2)+(-6))/2)`

`((5+3)/2 , (-2-6)/2)`

`((8)/2 , (-8)/2)` [Simplify your fractions by dividing]

(4 , -4)

To get a better understanding of this formula, remember that any number divided by 2 is the middle of that number. So what we are doing here is adding our points together and then dividing them by 2.
Here's a simple example:

What is the midpoint between (20 , 0) and (10 , 0)?

All I have to do is 20 + 10 = 30

and then divide by 2

`30 -: 2 = 15`

(15 , 0)

I know this is the right answer because I can add and subtract the same number from my midpoint to return to my two original points. In this case that number is 5.

15 + 5 = 20

15 - 5 = 10