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Given:

Lines x + 2y = 5 and x – 3y = 7, slope = 5.

To find:

The distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x – 3y = 7.

Concept Used:

Distance of a point from a line.

Explanation:

To find the point intersection of the lines x + 2y = 5 and x − 3y = 7, let us solve them.

⇒ x y

So, the equation of the line passing through with slope 5 is

⇒ 5y + 2 = 25x – 145

⇒ 25x – 5y – 147 = 0

Let d be the perpendicular distance from the point (1, 2) to the line 25x – 5y – 147 = 0

∴d

Hence, the required perpendicular distance is