The perpendicular distance from the point $$1$$,$$1$$ to the line which is perpendicular to $$4x$$−$$3y+1=0$$ and passing through $$3$$,$$5$$ is

Question

The perpendicular distance from the point $$1$$,$$1$$ to the line which is perpendicular to $$4x$$−$$3y+1=0$$ and passing through $$3$$,$$5$$ is

Infinity Learn · Accepted Answer

The equation of any line perpendicular to the line $$4x$$−$$3y+1=0$$ can be taken as $$3x+4y+k=0$$ It is passing through the point (3$$,$$5)It$$ implies $$33+45+k=09+20+k=0k=$$−$$29$$ Hence the equation of the line perpendicular to the line $$4x$$−$$3y+1=0$$ and passing through  the point $$(3$$,$$5) is $$3x+4y$$−$$29=0$$ 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$$,$$1) to the line $$3x+4y$$−$$29=0$$ is $$31+41$$−$$2916+9=225$$

The perpendicular distance from the point $(1, 1)$ to the line which is perpendicular to $4 x - 3 y + 1 = 0$ and passing through $(3, 5)$ is

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The perpendicular distance from the point 1,1 to the line which is perpendicular to 4x−3y+1=0 and passing through 3,5 is

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The perpendicular distance from the point $(1, 1)$ to the line which is perpendicular to $4 x - 3 y + 1 = 0$ and passing through $(3, 5)$ is