Question

If (P,2), (-3,4) and (7,-1) are collinear, then P=
​

Answer 1

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

$\textsf{The points (P,2),(-3,4) and (7,-1) are collinear}$

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

$\textsf{The value of P}$

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

$\underline{\mathsf{Concept\;used:}}$

$\mathsf{Slope\;of\;line\;joining\;(x_1,y_1)\;and\;(x_2,y_2)\;is}$

$\mathsf{\dfrac{y_2-y_1}{x_2-x_1}}$

$\textsf{Let the given 3 points be A(P,2),B(-3,4) and C(7,-1)}$

$\textsf{Since the points A,B and C are collinear, we have}$

$\textsf{Slope of AB=Slope of BC}$

$\mathsf{\dfrac{4-2}{-3-P}=\dfrac{-1-4}{7+3}}$

$\mathsf{\dfrac{2}{-3-P}=\dfrac{-5}{10}}$

$\mathsf{\dfrac{2}{-3-P}=\dfrac{-1}{2}}$

$\mathsf{4=3+P}$

$\mathsf{P=4-3}$

$\implies\boxed{\mathsf{P=1}}$

$\underline{\textsf{Answer:}}$

$\textsf{The value of P is 1}$

$\underline{\textsf{Find more:}}$

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