The ratio of MD to DN is equal to 2.
<h3>How to find the partition ratio for a line segment</h3>
In accordance with the image set aside, the locations of the points M and N are M(x, y) = (- 6, - 4) and N(x, y) = (6, 4), respectively. Now we determine the vectors associated to line segments MD and DN by vector sum:
<u>MD</u> = D(x, y) - M(x, y)
<u>MD</u> = (2, 4 / 3) - (- 6, - 4)
<u>MD</u> = (8, 16 / 3)
<u>DN</u> = N(x, y) - D(x, y)
<u>DN</u> = (6, 4) - (2, 4 / 3)
<u>DN</u> = (4, 8 / 3)
Lastly, we find the length of each line segment by Pythagorean theorem:
MD = √[8² + (16 / 3)²]
MD = (8 / 3)√13
DN = √[4² + (8 / 3)²]
DN = (4 / 3)√13
And the ratio of MD to DN is:
MD / DN = [(8 / 3)√13] / [(4 / 3)√13]
MD / DN = 2
The ratio of MD to DN is equal to 2.
<h3>Remark</h3>
The statement presents typing mistakes, we kindly present the correct form below:
<em>Point D is located on line segment MN at (2, 4 / 3). What ratio relates MD to DN?</em>
To learn more on line ratios: brainly.com/question/3148758
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