Question

Find the distance from point A(−14, 5) to the line −x+2y = 14.

Answer 1

Answer:

The distance from point A to given line is: 2√5 or 4.472 units

Step-by-step explanation:

Given equation of line is:

$-x+2y= 14$

And the point is:

$A = (x_1,y_1) = (-14,5)$

The standard form of equation of line is:

$Ax+By+C = 0$

Converting the given equation into standard form

$-x+2y-14=0$

The distance of a point (x1,y1) from a line is given by the formula:

$d = \frac{|Ax_1+By_1+C}{\sqrt{A^2+B^2}}$

In the given details,

A = -1, B = 2, C = -14

x1 = -14, y1 = 5

Putting the values in the formula

$d = \frac{|(-1)(-14)+(2)(5)-14|}{\sqrt{(-1)^2+(2)^2}}\\d = \frac{14+10-14}{\sqrt{1+4}}\\d = \frac{10}{\sqrt{5}}\\d = \frac{5*2}{\sqrt{5}}\\d = \frac{\sqrt{5}*\sqrt{5}*2}{\sqrt{5}}\\d = 2\sqrt{5}\\d = 4.472\ units$

Hence,

The distance from point A to given line is: 2√5 or 4.472 units