Question

The shortest distance of the point $(h,k)$ from both the axes are

• A. $|h|,|k|$
• B. $(h,k)$
• C. $\sqrt{h^2+k^2},0$
• D. none of these

Answer 1

The correct option is A $|h|,|k|$

Given the point is $(h,k).$

Now foot of the perpendicular

from $(h,k)$ on x-axis is $(h,0)$and

that on y-axis is $(0,k)$

Now the shortest distance between

$(h,k)$ and $(h,0)=\sqrt{(h-h{)}^2+(k-0{)}^2}$

$=|k|$ = the shortest distance of $(h,k)$ from x- axis.

Again the shortest distance between

$(h,k)$ and $(0,k)$ is

$\sqrt{(h-0{)}^2+(k-k{)}^2}=\left|h\right|$ = The shortest distance of $(h,k)$ from y-axis.