Question

The point M is the midpoint of LN where M(-12, 6) and N (-2,-5).

What are the coordinates of point L?

Answer 1

the person up top is correct

Answer 2

The coordinates of point L are:

(x₁, y₁) = (-22, 17)

Explanation:

We know that the Midpoint Formula is given by:

`\left(x,\:y\right)=\left((x_2+x_1)/(2),\:\:(y_2+y_1)/(2)\right)`

In our case:

M(-12, 6) is the midpoint. Thus,

(x, y) = (-12, 6)

N(-2, -5) is the second point, Thus,

(x₂, y₂) = (-2,-5)

We have to determine the coordinates of point L.

Let (x₁, y₁) be the coordinates of point L.

substituting (x, y) = (-12, 6), (x₂, y₂) = (-2,-5) in the Midpoint Formula

`\left(-12,\:6\right)=\left((-2+x_1)/(2),\:\:(-5+y_1)/(2)\right)`

Determining the x₁ coordinate of the point L

`(-2+x_1)/(2)=-12`

`-2+x_1=-24`

Add 2 to both sides

`-2+x_1+2=-24+2`

Simplify

`x_1=-22`

Determining the y₁ coordinate of the point L

`(-5+y_1)/(2)=6`

`-5+y_1=12`

Add 5 to both sides

`-5+y_1+5=12+5`

Simplify

`y_1=17\:\:\:`

Therefore, the coordinates of point L are:

(x₁, y₁) = (-22, 17)