The distance of the point (2$$, $$3) from the line $$2x$$ $$-$$ $$3y$$ $$+$$ $$9$$ $$=$$ $$0$$ measured along the line x $$-$$ y $$+$$ $$1$$ $$=$$ $$0$$, is

Question

The distance of the point (2$$, $$3) from the line $$2x$$ $$-$$ $$3y$$ $$+$$ $$9$$ $$=$$ $$0$$ measured along the line x $$-$$ y $$+$$ $$1$$ $$=$$ $$0$$, is

Infinity Learn · Accepted Answer

The slope of the line x $$-$$ y $$+$$ $$1$$ $$=$$ $$0$$ is $$1$$. So, it makes an angle of $$45$$° with $$x-axis$$.The equation of a line passing through (2$$, $$3) and making an angle of $$45$$° is given by   x−$$2cos$$⁡$$45$$∘$$=y$$−$$3sin$$⁡$$45$$∘$$=rCo-ordinates$$ of any point on this line are  $$2+rcos$$⁡$$45$$∘,$$3+rsin$$⁡$$45$$∘ or, $$2+r2$$,$$3+r2If$$ this point lies on the line $$2x-3y+9=0$$, then    $$4+r2$$−$$9$$−$$3r2+9=0$$⇒$$r=42Hence$$, required distance $$=42$$ units .

The distance of the point $(2, 3)$ from the line $2 x - 3 y + 9 = 0$ measured along the line $x - y + 1 = 0,$ is

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The distance of the point (2, 3) from the line 2x - 3y + 9 = 0 measured along the line x - y + 1 = 0, is

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The distance of the point $(2, 3)$ from the line $2 x - 3 y + 9 = 0$ measured along the line $x - y + 1 = 0,$ is