Question

What is the distance from point P(- 1, 1) to the line y = -2x + 4? Round to the nearest tenth.

Answer 1

Line equation: y = -2x + 4, Point (-1,1)

We have to write the equation in the standard form:

y = -2x + 4

-2x - y + 4 = 0

Now we can see the values of a, b, c and x0 and y0 to use the formulas

a = -2

b = -1

c = 4

x0 = -1

y0 = 1

Distance = abs(ax0 + by0 + c)/sqrt(a^2 + b^2) = abs(-2(-1) -1 (1) + 4)/sqrt((-2)^2 + (-1)^2) =

D = abs(2 - 1 + 4)/sqrt(4 + 1) = abs(5)/sqrt(5) = 5/2.236067 = 2.2360

Rounding to nearest tenth: Distance = 2.2

Answer: Distance is 2.2

`d\text{ = }\frac{\mathrm{abs}(ax_0+by_0+c)}{\sqrt[]{a^2+b^2}}`