Question

which of the lones 2x - y + 3 = 0 and x - 4y - 7 = 0 is farther from the origin​

Answer 1

Answer:

For checking which line is farther from origin we can find out individually the perpendicular distances to these lines from the point of origin.

So, for finding perpendicular distance to a line ax+by+c=0 from point (h,k) the formula is,

d = |ah+ky+c|/√a^2+b^2

So,First distance of origin from line 2x-y+3=0 will be

d1 = |2(0)-1(0)+3|/√2^2 + (-1)^2 = 3/√5

And, the distance of origin from line x-4y-7=0

will be

d2 = |1(0)-4(0)-7|/√1^2+(-4)^2 = 7/√17

So, now on comparing values of d1 and d2 we find that d2>d1

So, second line x-4y-7=0 is farther from point of origin than the first line 2x-y+3=0.

Hope this helps you !

Answer 2

Answer:

$For checking which line isfarther from origin we can find out individually the perpendicular distances to these lines from the point of origin. So, second line x-4y-7=0 is farther from point of origin than the first line 2x-y+3=0. Hope this helps you$