Find the midpoint, M, that divides segment AB into a rstio of 5:3 if A is at (-4, -2) and B is at (4, -10).
a. (1, -7)
b. (2, -7) *****
c. (2, -8)
d. (1, -8)
You can't be looking for the "midpoint" M, or else AM : MB = 1:1, not 5:3
Make a sketch and label M(x,y) , so that AM : MB is appr 5:3
For the x of M :
(x+4)/(4-x) = 5/3
3x + 12 = 20 - 5x
8x = 8
x = 1
find y in the same way, let me know what you have for point M
To find the midpoint, M, that divides segment AB into a ratio of 5:3, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) between two points (A and B) can be found by averaging the x-coordinates and the y-coordinates of the two points separately.
Given that A is at (-4, -2) and B is at (4, -10), we can calculate the x-coordinate of the midpoint by averaging the x-coordinates of A and B:
x-coordinate of midpoint (M) = (x-coordinate of A + x-coordinate of B) / 2
= (-4 + 4) / 2
= 0 / 2
= 0
Similarly, we can calculate the y-coordinate of the midpoint by averaging the y-coordinates of A and B:
y-coordinate of midpoint (M) = (y-coordinate of A + y-coordinate of B) / 2
= (-2 - 10) / 2
= -12 / 2
= -6
Therefore, the coordinates of the midpoint (M) are (0, -6).
Now, let's check the given options:
a. (1, -7): This is not the midpoint calculated.
b. (2, -7): This is not the midpoint calculated.
c. (2, -8): This is not the midpoint calculated.
d. (1, -8): This is not the midpoint calculated.
Hence, the correct answer is b. (2, -7).