Question

What is the midpoint between `B(3, -5, 6)` and `H(5,3,2)`?

Answer 1

See a 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, (color(red)(z_1) + color(blue)(z_2))/2)`

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

`(color(red)(x_1), color(red)(y_1), color(red)(z_1))` and `(color(blue)(x_2), color(blue)(y_2), color(blue)(z_2))`

Substituting gives:

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

`M_(BH) = (8/2 , -2/2, 8/2)`

`M_(BH) = (4, -1, 4)`

Answer 2

(4,-1,4)

Explanation:

for each of the corresponding x, y, and z coordinates:
-find the difference between them
- divide that difference by 2
- add to that coordinate for point B.

...for the x coordinate, you have `(5-3)/2 + 3`, so the x coordinate is 4. (4 is halfway between 3 and 5).

y coordinate: `(3-(-5))/2 + (-5) = -1` (-1 is halfway betwwen -5 and 3)

z coordinate: `(2 - 6)/2 + 6 = 4` (4 is halfway between 6 and 2)

GOOD LUCK

Answer 3

The midpoint is: `(4,-1,4)`

Explanation:

The midpoint between two points, `(x_1,y_1,z_1)` and `(x_2,y_2,z_2)` is:

`((x_1+x_2)/2,(y_1+y_2)/2,(z_1+z_2)/2)`

Applying this to the two given points:

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

`(4,-1,4)`