Question

Find the distance from point A(−1, 7) to the line y=3x. Round your answer to the nearest tenth.

Answer 1

Answer:

The distance from the point to the line is approximately 3.2 units

Step-by-step explanation:

Distance From a Point to a Line

Is the shortest distance from a given point to any point on an infinite straight line. The shortest distance occurs when the segment from the point and the line are perpendiculars.

If the line is given by the equation ax + by + c = 0, where a, b and c are real constants, the distance from the line to a point (x0,y0) is

$\displaystyle d= \frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}$

The line is given by the equation:

y=3x. We need to transform it into the specified form.

Subtracting 3x:

y - 3x = 0

Comparing with the general form of the line, we have

a=-3, b=1, c=0

The point (xo,yo) is (-1,7), thus:

$\displaystyle d= \frac{|-3\cdot (-1)+1\cdot 7+0|}{\sqrt{(-3)^2+1^2}}$

$\displaystyle d= \frac{|3+7|}{\sqrt{9+1}}$

$\displaystyle d= \frac{|10|}{\sqrt{10}}$

$\displaystyle d= \frac{10}{\sqrt{10}}$

$d\approx 3.2$

The distance from the point to the line is approximately 3.2 units