Question

A point lies on AB and 3/10 the distance from A to B. Point A is located at (5, 10) and point B is located at (20, 25).What are the coordinates of this point?(9 1/2,14 1/2)(9 1/2, 20 1/2)(15 1/2,20 1/2)(15 1/2, 20 1/2)

Answer 1

The coordinates of the point that lies between the two points (x1, y1) and (x2, y2) at the ratio m1: m2 from the first point to the second point is

$x=\frac{m_{1_{}}x_2+m_2x_1_{}}{m_1+m_2}$$y=\frac{m_1y_2+m_2y_1}{m_1+m_2}$

Since the point lies on 3/10 from points A and B, then

$\begin{gathered} m_1=3 \\ m_2=10-3=7 \end{gathered}$

Since the coordinates of A are (5, 10) and B are (20, 25), then

$\begin{gathered} x_1=5,x_2=20 \\ y_1=10,y_2=25 \end{gathered}$

Substitute them in the rules above to find the coordinates of the point of division

$\begin{gathered} x=\frac{(3)(20)+(7)(5)}{3+7} \\ x=\frac{60+35}{10} \\ x=\frac{95}{10} \\ x=9\frac{1}{2} \end{gathered}$

$\begin{gathered} y=\frac{3(25)+7(10)}{3+7} \\ y=\frac{75+70}{10} \\ y=\frac{145}{10} \\ y=14\frac{1}{2} \end{gathered}$

The coordinates of the point are (9 1/2, 14 1/2)

The answer is A