Find the point, M, that divides segment AB into a ratio of 4:7 if A is at (-33, 0) and B is at (0, 44).
A)(-22, 15)
B) (-22, 16)
C) (-21, 15)
D) (-21, 16)
Is it A?
no d
4+7 = 11
so for x
4/11 (0 - -33) + -33 = 12 +-33 = - 21
and for y
4/11(44-0) + 0 = 16
so
(-21 , 16)
To find the point M that divides segment AB into a ratio of 4:7, we can use the section formula. The section formula states:
M = ((7*A) + (4*B)) / (7 + 4)
where A and B are the coordinates of points A and B respectively.
Let's calculate the coordinates of point M using this formula.
A = (-33, 0)
B = (0, 44)
M = ((7 * (-33), 0) + (4 * (0, 44))) / (7 + 4)
= ((-231, 0) + (0, 176)) / 11
= (-231, 0 + 176) / 11
= (-231, 176) / 11
= (-21, 16)
So, the correct answer is D) (-21, 16).
To find the point, M, that divides segment AB into a ratio of 4:7, we can use the concept of section formula.
The section formula states that if a line segment AB is divided by a point M in the ratio of m:n, then the coordinates of M can be found using the following formula:
M(x, y) = [(Bx * m + Ax * n) / (m + n), (By * m + Ay * n) / (m + n)]
Given that A is (-33, 0), B is (0, 44), and the ratio is 4:7, we can substitute these values into the formula.
M(x, y) = [(0 * 4 + (-33) * 7) / (4 + 7), (44 * 4 + 0 * 7) / (4 + 7)]
Simplifying the equation:
M(x, y) = [(-231) / 11, (176) / 11]
M(x, y) = (-21, 16)
The correct answer is B) (-21, 16), not A).