Question

if a point A lies on x-axis and has abscissa(p+q) and another point B lies on y-axis and has ordinate (p-q),find distance between A and B​

Answer 1

The distance between points A and B is √[2(p²+q²)]

Step-by-step explanation:

Coordinate of the point A will be $(p+q,0)$

Coordinate of point B will be $(0,p-q)$

We know that distance between two points whose coordinates are $(x_1,y_1)$ and $(x_2,y_2)$ are is given by

$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Therefore, the distance between points A and B is

$d=\sqrt{(p+q-0)^2+(0-(p-q))^2}$

$\implies d=\sqrt{(p+q)^2+(p-q)^2}$

$\implies d=\sqrt{p^2+q^2+2pq+p^2+q^2-2pq}$

$\implies d=\sqrt{2p^2+2q^2}$

$\implies d=\sqrt{2(p^2+q^2)}$

Hope this answer is helpful.

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