Question

Find the distance between the point (0, 0) and the line with the equation -2x-y=3

Answer 1

\(\dfrac{|-2(0) - 1(0) - 3|}{\sqrt{(-2)^{2}+(-1)^{2}}} = \dfrac{3}{\sqrt{5}}\)

Answer 2

okay thank you!!! :)

Answer 3

i appreciat eyou showing me how to do it and also the answer how you got it

Answer 4

Or, if you want, you can find the line perpendicular to the given line and passing through the Origin.

y = -2x - 3

Slope is 1/2

y-0 = (1/2)(x-0) or y = (1/2)x

Solving, (1/2)x = -2x - 3
x = -4x - 6

5x = -6

x = -6/5
y = -3/5

Distance Formula: \(\sqrt{(-6/5)^{2}+(-3/5)^{2}} = \sqrt{\dfrac{36 + 9}{25}} = \dfrac{3\sqrt{5}}{5}\)

Same thing.