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( (n(x_1)+m(x_2))/(m+n) ,\, (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( (3(7.5)+2.3)/(1+3),\, (3(4.2)+5.4)/(1+3) \right) \\ \\ =\left( (22.5+2.3)/(4) ,\, (12.6+5.4)/(4) \right)=\left( (24.8)/(4) ,\, (18)/(4)\right) \\ \\ =(6.2,\, 4.5)`