What is the length of a segment with an endpoint of (-3, 1) and a midpoint of (8, 2)?

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What is the length of a segment with an endpoint of (-3, 1) and a midpoint of (8, 2)?

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Answer 1 · 2015-11-19T18:17:57

$(x_{2}, y_{2}) = (19, 3)$ $(x_2, y_2)=(19, 3)$

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,
$(x_{1}, y_{1}) = (- 3, 1)$ $(x_1, y_1)=(-3, 1)$
and
$(a, b) = (8, 2)$ $(a, b)=(8, 2)$

So,
$(x_{2}, y_{2}) = (2 (8) - (- 3), 2 (2) - 1)$ $(x_2, y_2)=(2color(red)((8)) -color(red)((-3)), 2color(red)((2))-color(red)1)$
$(x_{2}, y_{2}) = (16 + 3, 4 - 1)$ $(x_2, y_2)=(16+3, 4-1)$
$(x_{2}, y_{2}) = (19, 3)$ $(x_2, y_2)=(19, 3)$

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What is the length of a segment with an endpoint of (-3, 1) and a midpoint of (8, 2)?

1 Answer

Explanation:

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