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Question content area top Part 1 Find the midpoint of the line segment joining points A and B. A(8,-5) B(2,1) ​;

User Chif
by
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1 Answer

7 votes
7 votes

Answer:


(5,\, -2).

Explanation:

For a line segment in a plane, the
x-coordinates of the midpoint is the average of the
x\!-coordinates of the endpoints. Likewise, the
y-coordinates of the midpoint is the average of the
y\! coordinates of the endpoints.

For example, the midpoint of the line segment joining
(x_(a),\, y_(a)) and
(x_(b),\, y_(b)) is:


\begin{aligned} \left((x_(a) + x_(b))/(2),\, (y_(a) + y_(b))/(2)\right)\end{aligned}.

In this question,
x_(a) = 8,
x_(b) = 2,
y_(a) = (-5),
y_(b) = 1. Thus, the midpoint of the line segment joining the two points would be:


\begin{aligned} \left((8 + 2)/(2),\, ((-5) + 1)/(2)\right)\end{aligned}.

Simplify to obtain:


\begin{aligned} \left(5,\, -2\right)\end{aligned}.

Hence, the midpoint of the line segment joining
(8,\, -5) and
(2,\, 1) would be
(5,\, -2).

User Harsha Venkataramu
by
2.7k points