Find the point, M, that divides segment AB into a ratio of 3:2 if A is at (0, 15) and B is at (20, 0).
A) (9, 6)
B) (12, 6)
C) (12, 9)
D) (9, 12)
Is it b?
if not how do I find the answer?
SKETCH IT !!!!
3/2 in x and 3/2 in y
delta x = 20
3/5 (20) = 12
0 + 12 = 12
3/5 * ( 0-15) in y
delta y = -9
15 - 9 = 6
(12,6)
To find the point, M, that divides segment AB into a ratio of 3:2, you can use the formula:
M = ( (2*x2 + 3*x1) / (5), (2*y2 + 3*y1) / (5) )
Where (x1, y1) = coordinates of point A (0, 15) and (x2, y2) = coordinates of point B (20, 0).
Let's substitute the values:
M = ( (2*20 + 3*0) / 5, (2*0 + 3*15) / 5 )
= ( (40 + 0) / 5, (0 + 45) / 5 )
= ( 40 / 5, 45 / 5 )
= ( 8, 9 )
Therefore, the correct answer is C) (12, 9).
To find the point M that divides segment AB into a ratio of 3:2, we can use the concept of section formula in coordinate geometry.
Let's say the coordinates of point M are (x, y).
The section formula states that the coordinates of M can be calculated using the following equations:
x = ((2 * x2) + (3 * x1)) / (2 + 3)
y = ((2 * y2) + (3 * y1)) / (2 + 3)
Where (x1, y1) are the coordinates of point A, and (x2, y2) are the coordinates of point B.
Given A(0, 15) and B(20, 0), let's substitute the values into the formulas:
x = ((2 * 20) + (3 * 0)) / (2 + 3) = (40 + 0) / 5 = 40 / 5 = 8
y = ((2 * 0) + (3 * 15)) / (2 + 3) = (0 + 45) / 5 = 45 / 5 = 9
Therefore, the coordinates of point M are (8, 9).
Now let's check the options:
A) (9, 6) - This is not the solution we obtained.
B) (12, 6) - This is not the solution we obtained.
C) (12, 9) - This is not the solution we obtained.
D) (9, 12) - This is not the solution we obtained.
Therefore, the correct answer is none of the given options.