How to find the distance b/w the point (3,4) and the line 'y=-1'?

Question

Firstly i`m not able to put the line y=-1 into the form y=mx+b.

Y=mx+b
y=0(x)-1 or Y=m(0)-1 ??????
If i take y=m(0)-1 as correct then the slope is 'm' and the negetive reciprocal is -1/m (slope of the perpendicular)

Using the point (3,4) and the slope of the orthogonal line,
Y=mx+b

4=-1/m (3) +b
b=4+(3/m)

Answer 1

y = -1 is a horizontal line that contains the points (n, -1)

how far is (3, 4) from that line? Subtrace the y-coordinates: 4 - (-1) = 5

Answer 2

4 + 1 = 5

Answer 3

First, when writing the linear equation y = -1 in slope-intercept form, you assume the slope is 0, not the variable x. (If we were to set x = 0, that would be saying that every point on the line has an x-coordinate of 0 -- in other words, the line becomes a single point, (0, -1). )

Since y = -1 has a slope of zero, it's a flat (horizontal) line. A line perpendicular to it, then, will be perfectly vertical, and have no slope (or as they say nowadays, an "undefined slope").

So, we want to pass a vertical line through the point (3, 4) -- its equation winds up being x = 3, and it intersects the line y = -1 at (3, -1).

Finally, you can calculate the distance from (3, 4) to (3, -1) fairly easily.

Hope that helps!

Answer 4

Actually, you can make it in that form: m=0 and b=-1. Take the perpendicular slope (infinity), so the perpendicular line is of the form x=n. x=3 passes through (3,4) and is perpendicular to y=-1. So this is your line. x=3 and y=-1 intersect at (3,-1). The distance from this point to (3,4) is 5.

Answer 5

Well the SHORTEST distance from point (3,4) to the line y= -1 is 5, but since you didn't state at what point along the line you're talking about, the distance could be as high as infinity. Thus any distance between 5 and infinity is correct.

Answer 6

its 5. (4+1=5)

Answer 7

the gap is largely the prependicular drawn from the point (-a million,-3) to the line y=2 so inspite of the fee of x contained in the point it does no longer effect its distance from the line y=2 the gap is |(-3-2)/a| (the following a is the coefficent of y ie a million thus) so the ans. is 5.

Answer 8

The perpendicular line is x=a. where a is any real number. So, all you have to do is set x=x0 (which is 3).

Then the distance is y0-y1, 4-(-1) distance =5.

Answer 9

"For a line with
equation Ax + By + C = 0 and a point (r,s) the distance from the point to
the line is given by abs(Ar + Bs + C)/sqrt(A^2 + B^2). Here abs denotes
absolute value and sqrt denotes square root."

Answer 10

Just pick the point on the y=-1 line that is closest to you're other point like (3,-1).....its pretty simple from there.