Question

The midpoint of segment AB is M(-4, -3). If the coordinates of A are (-1, -2), what are the coordinates of B?

Answer 1

The formula to determine the midpoint of a segment or a line given the coordinates is:

`x_(midpoint)=(x_1+x_2)/(2)`
`y_(midpoint)=(y_1+y_2)/(2)`

Since we have the coordinate of the midpoint and one of the endpoints of the segment, let's plug it into the formula to get the coordinate of the other endpoint.

Let's start with the x-coordinates.

`-4=(-1+x_2)/(2)`

Then, solve for x₂.

`\begin{gathered} -8=-1+x_2 \\ -8+1=x_2 \\ -7=x_2 \end{gathered}`

Therefore, the x-coordinate of Point B is -7.

Let's move on to y-coordinates.

`-3=(-2+y_2)/(2)`

Then, solve.

`\begin{gathered} -6=-2+y_2 \\ -6+2=y_2 \\ -4=y_2 \end{gathered}`

Therefore, the y-coordinate of Point B is -4.

ANSWER:

Hence, the coordinates of B are (-7, -4).