Given midpoint and one endpoint find other endpoint

How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5,-6) and the midpoint M(1.5,4.5)?

Answer

Hint: The above question is based on the concept of line segment. The main approach towards solving this question is to find by using the midpoint formula of a line segment. Since we have already been given one endpoint and also the midpoint of the line segment then we can get the other point.

Complete step-by-step solution:
The above question is based on line segments. Line segments can be explained in such a way that for example a line has no endpoints but extends endlessly in both the directions. If you mark two points A and B on it and pick this segment separately, it becomes a line segment. The length between the endpoints is fixed.The length of the line segment is the distance between the endpoints. So, a line segment is a piece or part of a line having two endpoints
The formula to calculate the midpoint of a line segment is
\[M = \left( {\dfrac{{{x_1} + {x_2}}}{2},\dfrac{{{y_1} + {y_2}}}{2}} \right)\]
Where M is the midpoint and \[({x_1},{y_1})\] and \[\left( {{x_2},{y_2}} \right)\]
We have been given one endpoint and the midpoint so by substituting the values we get,
\[\left( {1.5,4.5} \right) = \left( {\dfrac{{ - 3.5 + {x_2}}}{2},\dfrac{{ - 6 + {y_2}}}{2}} \right)\]
To find \[{x_2}\] we need to solve the equation,
\[
   \Rightarrow 1.5 = \dfrac{{ - 3.5 + {x_2}}}{2} \\
   \Rightarrow 2 \times 1.5 = 2 \times \dfrac{{ - 3.5 + {x_2}}}{2} \\
   \Rightarrow {x_2} = - 3.5 + 3 \\
   \Rightarrow {x_2} = 6.5 \\
 \]
To find \[{y_2}\]we need to find this equation
\[
   \Rightarrow 4.5 = \dfrac{{ - 6 + {y_2}}}{2} \\
   \Rightarrow 2 \times 4.5 = 2 \times \dfrac{{ - 6 + {y_2}}}{2} \\
   \Rightarrow 9 = - 6 + {y_2} \\
   \Rightarrow {y_2} = 15 \\
 \]

Therefore, we get the other endpoint as \[\left( {6.5,15} \right)\].

Note: An important thing to note is that the fastest way to find missing endpoint is to determine distance from the known endpoint to midpoint and then performing the same transformation on midpoint.In this case known x values moves from -3.5 to 1.5.

Steps Download Article

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   Graph your values (optional). This will allow you to get a visual understanding of the linear equation. Make sure that you label your midpoint, .

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   Rewrite the x coordinate formula, substituting and .

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   Solve the remaining algebraic equation including isolating the variable. Perform the inverse operation on the constant to isolate the variable—and do it to both sides!

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