First slide

Equation of line in Straight lines

Question

The distance of the line 2x + 3y – 5 = 0 from the point (3, 5) along the line 5x – 3y = 0 in units is

Moderate

A

$\frac{2 \sqrt{34}}{21}$
B

$\frac{16}{21}$
C

$\frac{4 \sqrt{34}}{21}$
D

$\frac{3 \sqrt{43}}{21}$

Solution

Two lines intersect at the point $(\frac{5}{7}, \frac{25}{21})$
Distance of this point from the given point (3, 5) is
$\sqrt{{(3 - \frac{5}{7})}^{2} + {(5 - \frac{25}{21})}^{2}} = \frac{4 \sqrt{34}}{21}$

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