Julissa M.

asked • 08/27/20

Find the coordinates of N so that MN is 2/9 of MP.

The point N lies on the segment MP.

M (-3,4)

P(24,-32)

N(?,?)

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Raymond B. answered • 09/18/20

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(2/9) x (27) =6. Add 6 to-3 to get 3

2/9 x 36 = 8 Add 8 to 4 to get 12

the point is (3,12)


27 and 36 are the x coordinate differences and y coordinate difference, respectively

take 2/9 of each, add to the first point to get N coordinates (3,12)



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Adrienne C.

(3,12) is not on Segment MP. The equation for line MP in this problem will be (y-4)=-4/3(x+3) in point slope form. When (3,12) is substituted into this equation, you'll get a false statement. Since MP has a negative slope, y is decreasing while x is increasing. Therefore, while you will add the 6 to the x coordinate, you would actually subtract 8 from the y coordinate, giving you the coordinate (3,-4) for N. Not only is this on the line, you can check that the ratio is consistent using this distance formula. The length of MP is 45, meaning the distance of MN must be 10. (There's also a way more complicated way to do this, which would be to first calculate the length of MP, then calculate the length of MN, then to find the equation of the circle radius MN from M, then find the intersection point between circle M and MP. While this circle will intersect the line in two places, only one intersection point will be on the segment.)
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09/21/23

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