Question

Given directed line segment CD, if point E divides CD three-fourths of the way

Answer 1

Answer:

E(-2, -1.5)

Explanation:

From the diagram attached, the coordinates of point C and D are at C(1, 6) and D(-3,-4)

If a line segment AB with coordinates at $(x_1,y_1)\ and\ (x_2,y_2)$ is divided by a point O(x, y) in the ratio n:m, the coordinates of point O is given by the formula:

$x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1$

C(1, 6) and D(-3,-4)  are divided three fourths (in ratio 3:1) by point E. Let us assume E is at (x,y), hence the coordinate of point L is given as:

$x=\frac{n}{n+m}(x_2-x_1)+x_1=\frac{3}{4}(-3-1)+1=\frac{3}{4}(-4)+1=-2 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1=\frac{3}{4}(-4-6)+6=\frac{3}{4} (-10)+6=-1.5$

Point E is at (-2, -1.5)