Question

If the points (x y -3) (2 0 -1) and (4 2 3) lie on a straight line then what are the values of x and y respectively?​

Answer 1

$\textbf{Given:}$

$\text{Points are (x,y,-3), (2,0,-1) and (4,2,3) are collinear}$

$\textbf{To find:}$

$\text{The values of x and y}$

$\textbf{Solution:}$

$\text{We know that,}$

$\textbf{The equation of the line joining (x_1,y_1,z_1) and (x_2,y_2,z_2) is }$

$\bf\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}=\dfrac{z-z_1}{z_2-z_1}$

$\textbf{The equation of the line joining (2,0,-1) and (4,2,3) is }$

$\dfrac{x-2}{4-2}=\dfrac{y-0}{2-0}=\dfrac{z+1}{3+1}$

$\dfrac{x-2}{2}=\dfrac{y}{2}=\dfrac{z+1}{4}$

$\text{Since (x,y,-3) lies on this line,}$

$\dfrac{x-2}{2}=\dfrac{y}{2}=\dfrac{-3+1}{4}$

$\dfrac{x-2}{2}=\dfrac{y}{2}=\dfrac{-2}{4}$

$\dfrac{x-2}{2}=\dfrac{y}{2}=\dfrac{-1}{2}$

$\dfrac{x-2}{2}=\dfrac{-1}{2}\;\text{and}\;\dfrac{y}{2}=\dfrac{-1}{2}$

$\implies\;x-2=-1\;\text{and}\;y=-1$

$\implies\;x=2-1\;\text{and}\;y=-1$

$\implies\;x=1\;\text{and}\;y=-1$

$\therefore\textbf{The value of x is 1 and y is -1}$

Find more:

If (a,0) (b,0) (1,1) are these three points in a line than find the value of 1/a + 1/b = ​

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