P is the midpoint of the line segment AB. The coordinates of P are (5,-6). The coordinates of A are (-1,10). How do you find the coordinates of B?

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P is the midpoint of the line segment AB. The coordinates of P are (5,-6). The coordinates of A are (-1,10). How do you find the coordinates of B?

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Answer 1 · 2015-11-19T18:13:46

$B = (x_{2}, y_{2}) = (11, - 22)$ $B=(x_2, y_2)=(11, -22)$

Explanation:

If one end-point $(x_{1}, y_{1})$ $(x_1, y_1)$ and mid-point $(a, b)$ $(a, b)$ of a line-segment is known, then we can use mid-point formula to find the second end-point#(x_2, y_2).

How to use midpoint formula to find an endpoint?

$(x_{2}, y_{2}) = (2 a - x_{1}, 2 b - y_{1})$ $(x_2, y_2)=(2a-x_1, 2b-y_1)$

Here,
$(x_{1}, y_{1}) = (- 1, 10)$ $(x_1, y_1)=(-1, 10)$
and
$(a, b) = (5, - 6)$ $(a, b)=(5, -6)$

So,
$(x_{2}, y_{2}) = (2 (5) - (- 1), 2 (- 6) - 10)$ $(x_2, y_2)=(2color(red)((5)) -color(red)((-1)), 2color(red)((-6))-color(red)10)$
$(x_{2}, y_{2}) = (10 + 1, - 12 - 10)$ $(x_2, y_2)=(10+1, -12-10)$
$(x_{2}, y_{2}) = (11, - 22)$ $(x_2, y_2)=(11, -22)$

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P is the midpoint of the line segment AB. The coordinates of P are (5,-6). The coordinates of A are (-1,10). How do you find the coordinates of B?

1 Answer

Explanation:

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