Question

The coordinates of the endpoints of directed line segment ABC are A(-8,7) and C(7,-13). If AB:BC = 3:2, the coordinates of B are

Answer 1

Answer:

The coordinates of B are (1,-5).

Step-by-step explanation:

To find the coordinates of point $B$ we will apply section formula.

Its used to find out if any line segment is of any $m_1: m_2$ ratios.

As the lie segment is joining the points internally we will use section formula for internal points.

Lets say that $B$ is having coordinates $(k,l)$ then $k=\frac{m_1(x_2) +m_2(x_1)}{m_1+m_2}$ and $l=\frac{m_1(y_2) +m_2(y_1)}{m_1+m_2}$

Now we have $A=(8,7)$ we call it $(x_1,y_1)$ then $C=(7,-13)$ we call it $(x_2,y_2)$.

And $m_1=3$,$m_2=2$

Plugging all the values in section formula we have.

$k=\frac{m_1(x_2) +m_2(x_1)}{m_1+m_2}$

$k=\frac{3(7) +2(-8)}{2+3}$

$= \frac{21-16}{5}= 1$

Similarly

$l=\frac{m_1(y_2) +m_2(y_1)}{m_1+m_2}$

$l=\frac{3(-13) +2(7)}{2+3}$

$l=\frac{-39+14}{5}= -5$

So the coordinates of $B =(1,-5)$