Question

Find the point, M, that divides segment AB into a ratio of 53 if A is at (-4,-2) and B is at

(4, -10)
A). (1.-7)
B). (2-7)
c. (2,-8)
D). (1,-8)

Answer 1

To find point M that divides segment AB in a ratio of 5:3, use the section formula. Upon substitution, the coordinates of M are found to be (1, -7).

Step-by-step explanation:

The student is asking how to find the point, M, that divides the segment AB into a ratio of 5:3, given that point A is at (-4,-2) and point B is at (4, -10). To solve this, we can use the section formula for internal division:

Let M(x, y) be the point that divides AB in the ratio of 5:3. We can find the coordinates of M using the formula:

• x = ((m × x2) + (n × x1)) / (m + n)
• y = ((m × y2) + (n × y1)) / (m + n)

Here m = 5, n = 3, x1 = -4, y1 = -2, x2 = 4, and y2 = -10. Placing these values into the formula, we get:

• x = ((5 × 4) + (3 × (-4))) / (5 + 3) = (20 - 12) / 8 = 1
• y = ((5 × (-10)) + (3 × (-2))) / (5 + 3) = (-50 - 6) / 8 = -56 / 8 = -7

Therefore, the coordinates of point M are (1, -7).

The correct answer is option A). (1, -7).