Consider the points $A \equiv (3,\ 4),\ B \equiv (7,\ 13)$. If ‘$P$’ be a point on the line $y = x$, such that $PA + PB$ is minimum, then coordinates of $P$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Points $(3,\ 4)$ and (7, 13) are on the same side of straight line $y = x$. Take image of $A$ about $y = x\ ie,\ A^{''} \equiv (4,\ 3)$
[image:10_image37.emf]
Now, $P$ is a intersection point of line $y = x$ and $A^{''}B$
Equation of line $A^{''}B$ is $y - 3 = \frac{10}{3}(x - 4)$
$\Rightarrow 3y - 9 = 10x - 40$
$\Rightarrow 10x - 3y = 31$
$\Rightarrow \left( \frac{31}{7},\frac{31}{7} ight)\ satisfy\ the\ line\ A^{''}B\ such\ that\ PA + PB\ is\ minimum$
$	herefore Coordinates\ of\ P\ are\ \left( \frac{31}{7},\frac{31}{7} ight)$

Q. Consider the points $A \equiv (3,\ 4),\ B \equiv (7,\ 13)$. If ‘$P$’ be a point on the line $y = x$, such that $PA + PB$ is minimum, then coordinates of $P$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?