How do you find the missing coordinate if the 1st coordinate is (12, -8) and the midpoint is (3, 18)?

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How do you find the missing coordinate if the 1st coordinate is (12, -8) and the midpoint is (3, 18)?

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Answer 1 · 2018-04-13T14:16:58

$(- 6, 44)$ $(-6,44)$

Explanation:

$the coordinates of the midpoint are the average of the$ $"the coordinates of the midpoint are the average of the"$
$coordinates of the endpoints$ $"coordinates of the endpoints"$

$here one endpoint is (12, - 8)$ $"here one endpoint is "(12,-8)$

$let the endpoint to be found = (x, y)$ $"let the endpoint to be found "=(x,y)$

$\Rightarrow \frac{1}{2} (12 + x) = 3 \leftarrow x-coordinate of midpoint$ $rArr1/2(12+x)=3larrcolor(blue)"x-coordinate of midpoint"$

$multiply both sides by 2$ $"multiply both sides by 2"$

$\Rightarrow 12 + x = 6 \Rightarrow x = 6 - 12 = - 6$ $rArr12+x=6rArrx=6-12=-6$

$\Rightarrow \frac{1}{2} (- 8 + y) = 18 \leftarrow y-coordinate of midpoint$ $rArr1/2(-8+y)=18larrcolor(blue)"y-coordinate of midpoint"$

$multiply both sides by 2$ $"multiply both sides by 2"$

$\Rightarrow - 8 + y = 36 \Rightarrow y = 36 + 8 = 44$ $rArr-8+y=36rArry=36+8=44$

$\Rightarrow coordinates of missing endpoint = (- 6, 44)$ $rArr"coordinates of missing endpoint "=(-6,44)$

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How do you find the missing coordinate if the 1st coordinate is (12, -8) and the midpoint is (3, 18)?

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