Consider the point (x,y) lying on the graph of the line 2x+4y=5. Let L be the distance from point (x,y) to the origin. Write L as a function of x

Question

Consider the point (x,y) lying on the graph of the line  2x+4y=5. Let L be the distance from point (x,y) to the origin. Write L as a function of x

anonymous · Answer

Well, we know:
$$
d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
$$And we know the origin is at (0,0). So, this simplifies to:
$$
d=\sqrt{x_1^2+y_1^2}
$$Try to write y as a function of x, and substitute it into the formula.

anonymous · Answer

I got d=sqrt(x^2+((5-2x)^2/4^2))

anonymous · Answer

Yeah, now expand and simplify, and et voilá

anonymous · Answer

Stuck at $$d =\sqrt{x ^{2}+\left( \left( 5-2x \right)^{2}\div16 \right)}$$

anonymous · Answer

It's an ugly expression, I don't know if it is a requirement to simplify, but the answer you gave is correct.

anonymous · Answer

The book says its $$L = 20x ^{2}+20x +25$$

anonymous · Answer

I mean, we have, simplifications and all
$$
L=\frac{\sqrt{20x^2-20x+25}}{4}
$$But I don't see how the book ended without a fraction.

anonymous · Answer

Thats what I said! But one last thing, I don't understand how the 4 got as the denominator

anonymous · Answer

Since:
$$
\sqrt{16}=4
$$We can simply remove it from the radical and use the latter value. Sorry for responding so late! For some reason or another I can't see this thread's replies!