Question

Find the coordinates of point L that lies along the directed line segment from N(14, 4) to M(2, 8) and partitions the segment in the ratio of 1:3.A. (16, 12)B. (11, 5)C. (8, 6)D. (-3, 1)

Answer 1

`B.(11,5)`

Step-by-step explanation

We want to find L's coordinates that lie along the line between the points N(14, 4) and M(2, 8) and partitions the segment in the ratio of 1 : 3.

To do this, we have to apply the section formula:

`L=((m_1x_2+m_2x_1)/(m_1+m_2),(m_1y_2+m_2y_1)/(m_1+m_2))_{}`

where m₁ : m₂ is the ratio

(x₁, y₁) and (x₂ : y₂) are the two coordinates of the points

Therefore, we have that the coordinates of L are:

`\begin{gathered} L=(((1\cdot2)+(3\cdot14))/(1+3),((1\cdot8)+(3\cdot4))/(1+3)) \\ L=((2+42)/(4),(8+12)/(4)) \\ L=((44)/(4),(20)/(4)) \\ L=(11,5) \end{gathered}`

Those are the coordinates of L.