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Question
Find the distance of the point (–1, 1) from the line 12(x + 6) = 5(y – 2).
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Solution
12(x + 6) = 5(y – 2)
or 12x + 72 = 5y – 10
12x – 5y + 82 = 0
Distance of point (x1, y1) from the line ax + by + c = 0 `(("ax"_1 + "by"_1 + "c"))/sqrt("a"^2 + "b"^2)`
∴ Distance from point (−1, 1) to line 12x − 5y + 8 = 0
d = `(|12 xx (-1) - 5 xx 1 + 8|)/sqrt(12^2 + 5^2)`
= `|(12 - 5 + 82)/(sqrt(144 + 25))|`
= `65/13`
= 5 Units
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