Question

Line segment AB has endpoints A(7.5, 4.2) 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)    (3.6, 5.1)
B)    (5.1, 3.6)
C)    (4.5, 6.2)
D)    (6.2, 4.5

Answer 1

Given a line with endpoints $A(x_1,\, y_1)$ and $B(x_2,\, y_2)$, the coordinates of the point that divides the line segment directed from A to B in the ratio of m : n is given by

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

Given that line segment AB has endpoints A(7.5, 4.2) and B(2.3, 5.4). the coordinates of the point that divides the line segment directed from A to B in the ratio of 1 : 3 is given by

$(x,\, y)=\left( \frac{3(7.5)+2.3}{1+3},\, \frac{3(4.2)+5.4}{1+3} \right) \\ \\ =\left( \frac{22.5+2.3}{4} ,\, \frac{12.6+5.4}{4} \right)=\left( \frac{24.8}{4} ,\, \frac{18}{4}\right) \\ \\ =(6.2,\, 4.5)$