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Points A(−1.5) and B(6) are marked on a number line. Find the coordinate of point M if it is known that AM:MB=1:2. Find all possible answers.

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W0lf93
M can have a coordinate of (-9) or (1) There are potentially 3 different places for point M to go. It can be placed to the left of point A, between points A and B, and to the right of point B. Let's check those three possibilities. 1. Left of point A. This works if the distance between M and A is the same as the distance between A and B. So distance between A and B = 6 - (-1.5) = 6 + 1.5 = 7.5 So the location for M would be -1.5 - 7.5 = -9 So point M can have the value of -9. 2. Between A and B. This would also work. Since we want a 1:2 ratio, place M one third of the way from A to B. Since we already know the distance between A and B to be 7.5, that means that we should add 7.5/3 = 2.5 to the value of A. So -1.5 + 2.5 = 1 So point M can also have the value of 1. 3. To the right of point B This won't work. Point B will always be closer to M than point A will be. So it's impossible to get a ratio of 1:2.
abidemiokin

The possible coordinate of M is (11/3, 5/3)

The formula for calculating the midpoint of between two coordinates divided into the ratio m:n is expressed as:

[tex]M(x,y) =(\frac{mx_1+nx_2}{m+n}, \frac{my_1+ny_2}{m+n} )[/tex]

Given the coordinates of the A(−1.5) and B(6) divided in the ratio of 2:1, the coordinate of point M will be expressed as:

[tex]M(x,y) =(\frac{1(-1)+2(6)}{1+2}, \frac{1(5)+3(0)}{1+2} )\\M(x,y) =(\frac{-1+12}{3}, \frac{5+0}{3} )\\M(x,y) =(\frac{11}{3}, \frac{5}{3} )\\[/tex]

Hence the possible coordinate of M is (11/3, 5/3)

Learn more here: https://brainly.com/question/13989426

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