Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown

endpoint. Apply the midpoint formula, and solve the two equations for x and y.)
midpoint (-14,9), endpoint (-6,8)
The other endpoint is

Answer 1

(-22, 10)

Explanation:

So the midpoint equation is defined as:
`m=((x_1+x_2)/(2), (y_1+y_2)/(2))`. The order of the pairs don't matter since addition is associative, as long as you put the values where they are supposed to be (x in x spot, and y in the spot)

So, let's say the unknown end point is
`(x_2, y_2)`

We know what the midpoint is so we can solve for these values. Let's start with the x-value

`-14=(-6+x_2)/(2)`

Multiply both values by 2

`-28=-6+x_2`

Now add 6 to both sides

`-22=x_2`

Now let's do the same thing with the y-value

`9=(8+y_2)/(2)`

Multiply both sides by 2

`18=8+y_2`

Subtract 8 from both sides

`10=y_2`

So the other end point is
`(-22, 10)`