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 [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is divided by a point O(x, y) in the ratio n:m, the coordinates of point O is given by the formula:
[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1 \\\\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]
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:
[tex]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[/tex]
Point E is at (-2, -1.5)
