Question

Line segment AB has endpoints A( ) and B(2.3,5.4). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:3.

a) (0.5, 1.2)
b) (0.8, 1.8)
c) (1.1, 2.6)
d) (1.6, 3.6)

Answer 1

To find the coordinates of the point that divides the line segment AB in the ratio of 1:3, use the formula x=(x1*(n-m)+x2*m)/n and y=(y1*(n-m)+y2*m)/n, where (x1, y1) and (x2, y2) are the coordinates of points A and B, and m and n are the ratio numbers.

Step-by-step explanation:

To find the coordinates of the point that divides the line segment AB in the ratio of 1:3, we can use the formula:

x=(x1*(n-m)+x2*m)/n

y=(y1*(n-m)+y2*m)/n

Where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively, and m and n are the ratio numbers.

Here, (x1, y1) = (0, 0) and (x2, y2) = (2.3, 5.4), m = 1 and n = 3. Plugging in these values into the formula, we get:

x=(0*(3-1)+2.3*1)/3 = 0.7667

y=(0*(3-1)+5.4*1)/3 = 1.8

Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:3 is approximately (0.7667, 1.8).