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Dovator [93]
3 years ago
13

Find the distance from point A to the given line: A(-1, 7), y=3x How do I solve this?

Mathematics
1 answer:
kipiarov [429]3 years ago
3 0

he formula of a distance between a point (a, b)

and a line Ax + By + C = 0:

d=\dfrac{|Aa+Bb+C|}{\sqrt{A^2+B^2}}

We have the point A(-1, 7) → a = -1, b = 7

and the line y = 3x → 3x - y = 0 → A = 3, B = -1, C = 0.

Substitute:

d=\dfrac{|(3)(-1)+(-1)(7)+0|}{\sqrt{3^2+(-1)^2}}=\dfrac{|-3-7|}{\sqrt{9+1}}=\dfrac{|-10|}{\sqrt{10}}=\dfrac{10\sqrt{10}}{\sqrt{10}\cdot\sqrt{10}}\\\\=\dfrac{10\sqrt{10}}{10}=\sqrt{10}

<h3>Answer: d = √10</h3>
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