Question

Find the coordinates of point P along the directed line segment AB, from A(−2,−4) to B(6, 1), so that the ratio of AP to PB is 3 to 2

Answer 1

Answer:

helo guys its your answer

Step-by-step explanation:

Find the coordinates of the point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2

Answer 2

Given,

Coordinate of line segment AB $\[ = A\left( { - 2, - 4} \right),B\left( {6,1} \right)\]$

$\[\frac{{AP}}{{PB}} = \frac{3}{2}\]$

Solution,

If point $\[\left( {a,b} \right)\]$ divides the line segment $\[\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)\]$ in the ratio of $\[m:n\]$.

$\[\left( {a,b} \right) = \left( {\frac{{m{x_2} + n{x_1}}}{{m + n}},\frac{{m{y_2} + n{y_1}}}{{m + n}}} \right)\]$

Calculate the ratio of AP to PB.

Consider the coordinate of point p is $\[\left( {a,b} \right)\]$.

$\[\left( {a,b} \right) = \left( {\frac{{3 \times 6 + 2 \times \left( { - 2} \right)}}{{3 + 2}},\frac{{3 \times 1 + 2 \times \left( { - 4} \right)}}{{3 + 2}}} \right)\]$

$\[ \Rightarrow \left( {a,b} \right) = \left( {\frac{{18 - 4}}{5},\frac{{3 - 8}}{5}} \right)\]$

$\[ \Rightarrow \left( {a,b} \right) = \left( {\frac{{14}}{5},\frac{{ - 5}}{5}} \right)\]$

$\[ \Rightarrow \left( {a,b} \right) = \left( {\frac{{14}}{5}, - 1} \right)\]$

Hence the coordinate of point P is $\[\left( {\frac{{14}}{5}, - 1} \right)\]$.