Question

Find the point P that is 2/5 of the way from A to B on the directed line segment AB if A (-8, -2) and B (6, 19).Find the point P that is 2/5 of the way from A to B on the directed line segment AB if A (-8, -2) and B (6, 19).choice:(2.4, -6.4)(-7.2, -8.8)(7.2, 8.8)(-2.4, 6.4)

Answer 1

Given:

`\begin{gathered} Point\text{ P }(2)/(5)\text{ of the way to line AB} \\ A=(-8,-2) \\ B=(6,19) \end{gathered}`

Using the section formula;

`((m_1x_2+m_2x_1)/(m_2+m_1),(m_1y_2+m_2y_1)/(m_2+m_1))`

where;

`\begin{gathered} the\text{ ratio of }m_1:m_2=2:3 \\ \\ Hence, \\ m_1=2 \\ m_2=3 \\ x_1=-8 \\ y_1=-2 \\ x_2=6 \\ y_2=19 \end{gathered}`

Substituting the values into the formula;

`\begin{gathered} (((2*6)+(3*-8))/(3+2),((2*19)+(3*-2))/(3+2)) \\ =((12-24)/(5),(38-6)/(5)) \\ =((-12)/(5),(32)/(5)) \\ =(-2.4,6.4) \end{gathered}`

Therefore, the point P that is 2/5 of the way from A to B on the directed line segment AB is (-2.4, 6.4)