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a_sh-v [17]
3 years ago
7

point M divides AB so that AM:MB 1:2. If A has coordinates (-1,-3) and B has coordinates (8,9), what are the coordinates of M?

Mathematics
1 answer:
maria [59]3 years ago
5 0

Answer:

The coordinates of point M are (2,1)

Step-by-step explanation:

Let's call the coordinates of point M by (x, y)

We have that the rate AM:MB is 1/2, so we can calculate x and y as follows:

x-coordinate of A is equal to -1, and x-coordinate of B is equal to 8, then:

AM:MB = [x - (-1)] / [8 - x] = 1/2

(x+1)/(8-x) = 1/2

2x+2 = 8-x

3x = 6

x = 2

y-coordinate of A is equal to -3, and y-coordinate of B is equal to 9, then:

AM:MB = [y - (-3)] / [9 - y] = 1/2

(y+3)/(9-y) = 1/2

2y+6 = 9-x

3y = 3

y = 1

So the coordinates of point M are x = 2 and y = 1 or (2,1)

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2) To find y we are going to use the trigonometric function tangent. Remember that tan(y)= \frac{opposite}{adjacent}. We know that the opposite side of our angle y is 8, and its adjacent side is 10, so lets replace those values in our tangent function to find y:
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3) Finally, to find z we are going to take advantage of two facts: the sum of the interior angles of a triangle is always 180°, and  our triangle is a right one, so one of its sides is 90°. Therefore, y+z+90=180. Since we already know the value of y, lets replace it in our equation and solve for z:
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