The perpendicular distance from $$1$$,$$3$$ to the line passing through the point $$P2$$,$$1$$ where the point $$P2$$,$$1$$ bisects the portion of the line intercepted between the axes.

Question

The perpendicular distance from $$1$$,$$3$$  to the line passing through the point $$P2$$,$$1$$ where the point $$P2$$,$$1$$ bisects the portion of the line intercepted between the axes.

Infinity Learn · Accepted Answer

The equation of the line whose portion intercepted between the axes bisected by $$x1$$,$$y1$$ is $$xx1+yy1=2$$ Hence the equation of the line whose portion intercepted between the axes at $$P(2$$,$$1)$$ is $$x2+y=2$$ Rewrite the equation as $$x+2y$$−$$4=0$$ The perpendicular distance from a point $$Px1$$,$$y1$$ to the line $$ax+by+c=0$$ is $$ax1+by1+ca2+b2$$ The perpendicular distance from a point (1$$,$$3) to the line $$x+2y$$−$$4=0$$ is $$1+23$$−$$41+4=35=355$$

The perpendicular distance from $(1, 3)$ to the line passing through the point $P (2, 1)$ where the point $P (2, 1)$ bisects the portion of the line intercepted between the axes.

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The perpendicular distance from 1,3 to the line passing through the point P2,1 where the point P2,1 bisects the portion of the line intercepted between the axes.

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The perpendicular distance from $(1, 3)$ to the line passing through the point $P (2, 1)$ where the point $P (2, 1)$ bisects the portion of the line intercepted between the axes.