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What has 2 o's 2 n 's an l and a d?

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Anonymous

12y ago
Updated: 8/17/2019

London

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12y ago

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the points L, M and N are such that LMN is a straight line. the coordinates of L are (-3, 1)the coordinates of M are (4, 9)given that LM:MN=2:3find the coordinates of N?

First, we can use the distance formula to find the length of LM: d(L,M) = sqrt((4 - (-3))^2 + (9 - 1)^2) = sqrt(49 + 64) = sqrt(113) Since LM:MN = 2:3, we can express the distance from L to N as (3/2) times the distance from L to M: d(L,N) = (3/2) * d(L,M) = (3/2) * sqrt(113) To find the coordinates of N, we need to determine the direction from M to N. We know that LMN is a straight line, so the direction from M to N is the same as the direction from L to M. We can find this direction by subtracting the coordinates of L from the coordinates of M: direction = (4 - (-3), 9 - 1) = (7, 8) To find the coordinates of N, we start at M and move in the direction of LMN for a distance of (3/2) * d(L,M): N = M + (3/2) * d(L,M) * direction / ||direction|| where ||direction|| is the length of the direction vector, which is: ||direction|| = sqrt(7^2 + 8^2) = sqrt(113) Substituting the values, we get: N = (4, 9) + (3/2) * sqrt(113) * (7/sqrt(113), 8/sqrt(113)) Simplifying, we get: N = (4 + (21/2), 9 + (24/2)) = (14.5, 21) Therefore, the coordinates of N are (14.5, 21). Answered by ChatGPT 3


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