Question

A point Q on a segment with endpoints A(2, -1) and C(4, 2) partitions thesegment in a 3:1 ratio. Find Q.

Answer 1

dividesThe rule of the point Q = (x, y), that divide the line segment AB to the ratio 3: 1 is

$\begin{gathered} x=\frac{m1x2+m2x1}{m1+m2} \\ y=\frac{m1y2+m2y1}{m1+m2} \end{gathered}$

A = (2, -1), then

x1 = 2 and y1 = -1

B = (4, 2), then

x2 = 4 and y2 = 2

The ratio is 3: 1, then

m1 = 3 and m2 = 1

We will substitute them in the rules above

$x=\frac{3(4)+1(2)}{3+1}=\frac{12+2}{4}=\frac{14}{4}=3.5$

The x-coordinate of point Q is 3.5

$\begin{gathered} y=\frac{3(2)+1(-1)}{3+1}=\frac{6-1}{4}=\frac{5}{4} \\ y=1.25 \end{gathered}$

The y-coordinate of point Q is 1.25

The coordinates of point Q are (3.5, 1.25)