Question

What is the distance between the origin and the midpoint of `(1, 2)` and `(-3, 6)`?

Answer 1

`sqrt(17)` or `4.123` rounded to the nearest thousandth.

Explanation:

First, we use this formula to find the midpoint of these two points:

`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)(1) + color(blue)(-3))/2 , (color(red)(2) + color(blue)(6))/2) = (-2/2 , 8/2) = (-1, 4)`

Next, we can use the distance formula to find the distance between the origin, which is (0, 0) and (-1, 4). The formula for calculating the distance between two points is:

`d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)`

Substituting the values from the points in the problem gives:

`d = sqrt((color(red)(-1) - color(blue)(0))^2 + (color(red)(4) - color(blue)(0))^2) = sqrt((-1)^2 + 4^2) = sqrt(1 + 16) =`

`sqrt(17)` or `4.123` rounded to the nearest thousandth.