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Nadya [2.5K]
3 years ago
10

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

Geography
1 answer:
Kazeer [188]3 years ago
7 0

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)

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