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GradeDistance between a Point and a Line

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Find the distance of the line $$4x + 7y + 5 = 0$$ from the point $$\left( {1,2} \right)$$ along the line $$2x - y = 0$$.

A. $$\dfrac{{23}}{7}\sqrt 5 $$ sq units

B. $$\dfrac{{23}}{{18}}\sqrt 5 $$ sq units

C. $$\dfrac{{23}}{8}\sqrt 5 $$ sq units

D. None of these

A. $$\dfrac{{23}}{7}\sqrt 5 $$ sq units

B. $$\dfrac{{23}}{{18}}\sqrt 5 $$ sq units

C. $$\dfrac{{23}}{8}\sqrt 5 $$ sq units

D. None of these

The distance of the lines \[2x-3y=4\]from the point \[(1,1)\] measured parallel to the line \[x+y=1\] is

1) \[\sqrt{2}\]

2) \[\dfrac{5}{\sqrt{2}}\]

3) \[\dfrac{1}{\sqrt{2}}\]

4) \[6\]

1) \[\sqrt{2}\]

2) \[\dfrac{5}{\sqrt{2}}\]

3) \[\dfrac{1}{\sqrt{2}}\]

4) \[6\]

Find the perpendicular distance of a point P (5, 7) from the y-axis.

How do you find in radical form, the distance between the two points (-3,7) and (4,2)?

Show that of all line segments drawn from a point to a line which is not on it, the perpendicular distance is the shortest distance.

What is the distance of the point (p,q,r) from the x-axis?

Find the equation of the locus of a point $ P $ which is equidistant from the straight line $ 3x - 4y + 2 = 0 $ and the origin

Find the distance of point \[\left( 1,-5,9 \right)\] from plane \[x-y+z=5\] measured along the line \[x=y=z\].

Find the difference of the maximum and the minimum distance of a point on the line $x+y-1=0$, where it cuts x-axis with respects to the circle ${{x}^{2}}+{{y}^{2}}-6x-8y+24=0$?

(a) 1,

(b) 2,

(c) $2\sqrt{5}$,

(d) $3\sqrt{5}$.

(a) 1,

(b) 2,

(c) $2\sqrt{5}$,

(d) $3\sqrt{5}$.

The shortest distance from the line \[3x\text{ + 4y = 25}\] to the circle \[{{x}^{2}}\text{ + }{{\text{y}}^{2}}\text{ = 6x - 8y}\] is equal to

\[\begin{align}

& A.\dfrac{1}{2} \\

& B.\dfrac{7}{5} \\

& C.\dfrac{11}{5} \\

& D.\dfrac{1}{3} \\

\end{align}\]

\[\begin{align}

& A.\dfrac{1}{2} \\

& B.\dfrac{7}{5} \\

& C.\dfrac{11}{5} \\

& D.\dfrac{1}{3} \\

\end{align}\]

Find the distance of the point (1,1) from the line $ 12\left( x+6 \right)=5\left( y-2 \right) $ .

Find the distance of the point \[P(-1,5)\] from x-axis.

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