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A line segment has an endpoint at (3,2). if the midpoint of the line segment is (6,-2), what are the coordinates of the point at the other end of the line segment?

User Ghost Ops
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1 Answer

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We are given that the end-point of a line segment is (3, 2) and the middle point is (6, -2).

The formula for the middle point of a line segment is given by:


(h,k)=((x_1+x_2)/(2),(y_1+y_2)/(2))

Where "h" and "k" are the middle points of the segment.

Now, we can set each of the coordinates equal. For the x-coordinates we have:


h=(x_1+x_2)/(2)

Where:


x_1,x_2=\text{ coordinates of the end-points}

Now, we solve for the second end-point.

First, we multiply both sides by 2:


2h=x_1+x_2

Now, we subtract x1 from both sides:


2h-x_1=x_2

Now, we substitute both sides:


\begin{gathered} 2(6)-3=x_2 \\ 12-3=x_2 \\ 9=x_2 \end{gathered}

Now, we solve for the y-coordinate:


k=(y_2+y_1)/(2)

Now, we multiply both sides by 2 and subtract the first coordinate to both sides:


2k-y_1=y_2

Now, we plug in the values:


\begin{gathered} 2(-2)-2=y_2 \\ -4-2=y_2 \\ -6=y_2 \end{gathered}

Therefore, the coordinates of the other end-point is:


(x_2,y_2)=(9,-6)

User Victoria Agafonova
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