Question

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

from C to D. find the coordinates of E. Round to the nearest tenth.

Answer 1

E(-2, -1.5)

Step-by-step 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=(n)/(n+m)(x_2-x_1)+x_1 \\\\y=(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=(n)/(n+m)(x_2-x_1)+x_1=(3)/(4)(-3-1)+1=(3)/(4)(-4)+1=-2 \\\\y=(n)/(n+m)(y_2-y_1)+y_1=(3)/(4)(-4-6)+6=(3)/(4) (-10)+6=-1.5`

Point E is at (-2, -1.5)