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

ANSWER

$B.(11,5)$

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:

$L=(\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2})_{}$

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:

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

Those are the coordinates of L.