Question

Point D is located on MN at (2,43). What ratio relates MD to DN?

Answer 1

The ratio of MD to DN is equal to 2.

How to find the partition ratio for a line segment

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:

MD = D(x, y) - M(x, y)

MD = (2, 4 / 3) - (- 6, - 4)

MD = (8, 16 / 3)

DN = N(x, y) - D(x, y)

DN = (6, 4) - (2, 4 / 3)

DN = (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.

Remark

The statement presents typing mistakes, we kindly present the correct form below:

Point D is located on line segment MN at (2, 4 / 3). What ratio relates MD to DN?

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