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

Answer 1

This would involve using the distance formula. I can't remember the formula exactly. But that should help you solve it.

Answer 2

d = √(x² + y²)

Now, since (x,y) lies on the line 2x + 4y = 5 you can solve for y in terms of x to get

y = (5-2x)/4

Now square y,

y² = (5 - 2x)²/16

Substitue this into the formula for d above

d = √(x² + (5 - 2x)²/16 )

Within the radical, combine over a common denominator of 16

d = √(16x² + (5 - 2x)² )/16

Factor out the radical 1/16, which is ¼,

d = ¼ √(16x² + (5 - 2x)² )

Now, expand the binomial inside the radical and simplify,

d = ¼ √(16x² + 25 - 20x + 4x² )

d = ¼ √(20x² - 20x + 25)