Question

If the points $(5,5),(7,7)$ and $(a,8)$ are collinear, then the value of $a$ is ___ .

• A. $6$
• B. $3$
• C. $8$
• D. $7$

Answer 1

Answer: (C)

$8$

If all the above points are collinear, then they must lie on a single line.

The equation of the line passing through the points $(5,5)$ and $(7,7)$ is
$\frac{y-7}{x-7}=\frac{y-5}{x-5}$ or $y=x$. ( hint: equating the slopes of line formed by these three points)

Thus the x coordinate when the y coordinate is $8$ is $8-a=0$ or $a=8$.

Hence the point is $(8,8)$.