Find the point, M, that divides segment AB into a ratio of 2:1 if A is at (-1, 2) and B is at (8, 15).
A(-1, 2), M(x, y), B(8, 15).
x+1 = 2/3(8+1)
X = 5.
y-2 = 2/3(15-2)
Y = 32/3.
To find the point M that divides segment AB into a ratio of 2:1, we can use the section formula.
Let's label the coordinates of point M as (x,y).
The section formula states that:
x = (x2 * m + x1 * n) / (m + n)
y = (y2 * m + y1 * n) / (m + n)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, and m and n are the ratios.
Given:
A = (-1, 2)
B = (8, 15)
Ratio 2:1
Letting m = 2 and n = 1, we can substitute the values into the formula.
x = (8 * 2 + (-1) * 1) / (2 + 1) = (16 - 1) / 3 = 15 / 3 = 5
y = (15 * 2 + 2 * 1) / (2 + 1) = (30 + 2) / 3 = 32 / 3
Thus, the point M that divides segment AB into a ratio of 2:1 is (5, 32/3).
To find the point M that divides segment AB into a ratio of 2:1, you can use the section formula.
The section formula states that the coordinates of a point M that divides the segment AB with endpoints (x1, y1) and (x2, y2) into a ratio of m:n can be found using the following formula:
M = ((nx2 + mx1) / (m + n), (ny2 + my1) / (m + n))
In this case, A is (-1, 2) and B is (8, 15). The ratio is 2:1, which means m = 2 and n = 1.
Plugging in the values into the formula, we get:
M = ((1*8 + 2*(-1)) / (2+1), (1*15 + 2*2) / (2+1))
= ((8 - 2) / 3, (15 + 4) / 3)
= (6 / 3, 19 / 3)
= (2, 6.333)
Therefore, the point M that divides segment AB into a ratio of 2:1 is approximately (2, 6.333).
x-coordinate ... 2/3 of the way from -1 to 8 ... 6 units from -1 ... 5
y-coordinate ... 2/3 of the way from 2 to 15 ... 26/3 units from 2 ... 20/3