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B. M is the midpoint of AB. If A = (4,1) and M = (-3,-3), find the coordinates of

the other endpoint, B.

1 Answer

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Answer:


(-10,\, -7).

Explanation:

If
A\; (x_(a),\, y_(a)) and
B\; (x_(b),\, y_(b)) are the two endpoints of a line segment, the midpoint of that line segment will be at:


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

In other words, the
x-coordinate of the midpoint will be
(1/2)\, (x_(a) + x_(b)) while the
y-coordinate of the midpoint will be
(1/2)\, (y_(a) + y_(b)).

In this question, it is given that point
A is at
(4,\, 1), such that
x_(a) = 4 and
y_(a) = 1, while
x_(b) and
y_(b) need to be found.

The midpoint is at
(-3,\, -3), with an
x-coordinate of
(-3) and a
y-coordinate of
(-3). Substitute these values into the midpoint equation and solve for
x_(b) and
y_(b):


(1/2)\, (4 + x_(b)) = (-3).


x_(b) = (-10)


(1/2)\, (1 + y_(b)) = (-3).


y_(b) = (-7).

Therefore, point
B will be at
(-10,\, -7).

User Rousonur Jaman
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