What are the coordinates of point P, that lies $\frac{1}{5}$ $1/5$ of the way from $A (- 7, - 35)$ $A(-7,-35)$ to $B (8, - 5)$ $B(8, -5)$ ?

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What are the coordinates of point P, that lies $\frac{1}{5}$ $1/5$ of the way from $A (- 7, - 35)$ $A(-7,-35)$ to $B (8, - 5)$ $B(8, -5)$ ?

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Answer 1 · 2018-04-27T03:08:58

$P = (- 4, - 29)$ $P=(-4,-29)$

Explanation:

Section formula :
If a point $P (x, y)$ $P(x,y)$ divides a line segment joining $A (x_{1}, y_{1}) and B (x_{2}, y_{2})$ $A(x_1,y_1) and B(x_2,y_2)$ in the ratio $m : n$ $m:n$ , i.e., $A P : P B = m : n$ $AP:PB=m:n$ ,
then $P (x, y) = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$ $P(x,y)=((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n))$
Given $A P : P B = m : n = \frac{1}{5} : \frac{4}{5} = 1 : 4$ $AP:PB=m:n=1/5:4/5=1:4$
$\Rightarrow P (x, y) = (\frac{(1 \times 8) + (4 \times - 7)}{1 + 4}, \frac{(1 \times - 5) + (4 \times - 35)}{1 + 4})$ $=> P(x,y)=(((1xx8)+(4xx-7))/(1+4)," " ((1xx-5)+(4xx-35))/(1+4))$
$= (- 4, - 29)$ $=(-4,-29)$
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What are the coordinates of point P, that lies $\frac{1}{5}$ $1/5$ of the way from $A (- 7, - 35)$ $A(-7,-35)$ to $B (8, - 5)$ $B(8, -5)$ ?

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