Question

Find the coordinates of point M, that partitions the directed line segment SY from S(4,2) to Y(-4,-6) in a ratio of 1/3.

Answer 1

Answer:

the coordinates of  point M = (2,0)

Step-by-step explanation:

Given;

point S along the segment, = S(4,2)

point Y along the segment, = Y(-4, -6)

ratio of the partition = ¹/₃

total ratio = 1 + 3 =  4

The midpoint of segment SY is calculated as follows;

$mid-point (o) = \frac{x_1 + x_2}{2} ,\ \frac{y_1 + y_2}{2}\\\\ mid-point (o) = \frac{4 + (-4)}{2} , \ \frac{2+ (-6)}{y} \\\\mid-point (o) = \frac{0}{2} , \ \frac{-4}{2} \\\\mid-point (o) = (0, \ -2)$

The coordinates of point M is calculated as follows;

point M divides the segment into 4 equal parts with point O as the mid-point.

                M

S--------------|-------------------O-------------------|-------------------Y

|SO| = |OY|

$The \ mid-point \ of \ SO = M\\\\Point \ S = (4,2) \\\\Point \ O = (0,-2) \\\\Point \ M = \frac{4 + 0}{2}, \frac{2 - 2}{2} \\\\ Point \ M = 2, 0 \\\\M = (2,0)$

Therefore, the coordinates of  point M = (2,0)