Search any question & find its solution
Question:
Answered & Verified by Expert
By using the concept of equation of a line, prove that the three points $(3,0),(-2,-2)$ and $(8,2)$ are collinear.
Solution:
2596 Upvotes
Verified Answer
Equation of the line passing through $(3,0)$ and $(-2,-2)$ is
$y-0=\frac{-2-0}{-2-3}(x-3) \Rightarrow y=\frac{2}{5}(x-3)$
$\Rightarrow 5 y=2 x-6 \Rightarrow 2 x-5 y=6$
If the point $(8,2)$ lies on it, $(8,2)$ will satisfy the equation of the lines.
LHS $=2 \times 8-5 \times 2=16-10=6=$ RHS
Hence $(8,2)$ lies on it
$\therefore(3,0),(-2,-2)$ and $(8,2)$ are collinear.
$y-0=\frac{-2-0}{-2-3}(x-3) \Rightarrow y=\frac{2}{5}(x-3)$
$\Rightarrow 5 y=2 x-6 \Rightarrow 2 x-5 y=6$
If the point $(8,2)$ lies on it, $(8,2)$ will satisfy the equation of the lines.
LHS $=2 \times 8-5 \times 2=16-10=6=$ RHS
Hence $(8,2)$ lies on it
$\therefore(3,0),(-2,-2)$ and $(8,2)$ are collinear.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.