Q:

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

Accepted Solution

A:
Answer:The distance from the point to the line is approximately 3.2 unitsStep-by-step explanation:Distance From a Point to a LineIs 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 = 0Comparing with the general form of the line, we havea=-3, b=1, c=0The 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