Question

point P lies on a line segment AB. AP is 4/7th of BP. P lies at (-3, 15) and A lies at (-11, 7). what are the coordinates of B?​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{P(-3,15) is a point on AB and A(-11,7)}$

$\mathsf{AP=\dfrac{4}{7}BP}$

$\underline{\textsf{To find:}}$

$\textsf{Coordinates of B}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{AP=\dfrac{4}{7}BP}$

$\mathsf{\dfrac{AP}{BP}=\dfrac{4}{7}}$

$\implies\textsf{P divides AB internally in the ratio 4:7}$

$\textsf{Then, by section formula}$

$\mathsf{(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})=(-3,15)}$

$\mathsf{(\dfrac{4x_2+7(-11)}{4+7},\dfrac{4y_2+7(7)}{4+7})=(-3,15)}$

$\mathsf{(\dfrac{4x_2-77}{11},\dfrac{4y_2+49}{11})=(-3,15)}$

$\implies\mathsf{\dfrac{4x_2-77}{11}=-3\;\;\&\;\;\dfrac{4y_2+49}{11}=15}$

$\implies\mathsf{4x_2-77=-33\;\;\&\;\;4y_2+49=165}$

$\implies\mathsf{4x_2=77-33\;\;\&\;\;4y_2=165-49}$

$\implies\mathsf{4x_2=44\;\;\&\;\;4y_2=116}$

$\implies\mathsf{x_2=\dfrac{44}{4}\;\;\&\;\;y_2=\dfrac{116}{4}}$

$\implies\mathsf{x_2=11\;\;\&\;\;y_2=29}$

$\therefore\textsf{The coordinates of B are(11,29)}$

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