Question

If $P,Q,R$ are the collinear points such that $P(7,7),Q(3,4)$ and $PR=10$, find the coordinates of $R$.

Answer 1

Given, Point $P(7,7),Q(3,4),R(h,k)$ are collinear

$\therefore \frac{4-7}{3-7}=\frac{k-4}{h-3}$

= $\frac{3}{4}=\frac{k-4}{h-3}$ ...(I)

It gives, $k=\frac{3h+7}{4}$

Also, ${(h-7)}^2+{(k-7)}^2=100$ ...(II) $\because PR=10$

Now, by substituting the value of k in equation 2 and we got the resultant quadratic equation as follows:

$h^2-14h-15=0$

Now by solving the above quadratic equation we got,

$\therefore h=15$ or $h=-1$

$k=13$ or $k=1$

$\therefore$ The point R can be $(15,13)$ & $(-1,1)$