the distance formula from a point to a line is absAx+By+c/sqrtA^2+B^2. But what do you plug in?

Question

my problem is: Find distance from point P(-1, 4) to the line 2x - 3y = 4 to the nearest hundred. I just don't know what numbers to plug in.

Answer 1

you need to understand what the equation means. Formulas are useless unless you understand them. If you have a line represented by the equation Ax + By + c = 0 and you have a point (X, Y), then at the closest point on the line to (X,Y), the distance is given by the formula you showed with the line coefficients A, B, c and the point coordinates X, Y. If you do't understand this, get help, not just plug things in thatyou don't understand.

Answer 2

you ought to use the gap formula, yet in the past leaping to that i might have was hoping which you will have asked, which distance? A distance between 2 factors can in basic terms be one component, yet a line is composed of infinitely many factors, so which element can we decide on? properly, the respond is, we decide on the element closest to (3,-5). So while asked to discover the "distance" between 2 gadgets the place there could be an arbitration of the gap, we are implicitly being asked for the minimal distance, the shortest distance. With all that being stated, particular, you ought to use the gap formula. you will have 2 factors. the 1st is obviously (3,-5), the 2d may be a element on the line that's of the kind (x,y) = (x, 4x - one million). so which you will plug all that throughout, then discover the minimal of that function. Now, that technique works in simple terms effective, yet there is an extra handy way. what's the shortest distance between 2 factors? Did you assert a in the present day line? stable. yet we could bypass one step extra suitable. what variety of line? i'm making a wager you're able to not answer that one. properly, the respond is a common, or perpendicular, line. Draw a photograph of this concern and start up drawing strains by way of (3,-5) and noting the place they intersect y = 4x - one million. you're able to be able to tell visually that the shortest line section between (3,-5) and the place it intersects y = 4x - one million is unquestionably perpendicular to y = 4x - one million. So we could come across a line that's perpendicular to 4x - one million and is composed of (3, -5). Then we are able to discover the place that crosses 4x - one million after which you have 2 factors which will properly be plugged into the gap formula. (i comprehend this sounds like extra steps, and it extremely is, however the stairs are extra handy). strains perpendicular to 4x - one million have the kind y = (-x/4) + b This could bypass by way of (3,-5): -5 = (-3/4) + b ? b = -17/4 the place do those strains flow? 4x - one million = (-x/4) - (17/4) 16x - 4 = -x - 17 17x = -13 x = -13/17 y = 4(-13/17) - one million = -sixty 9/17 Now in simple terms discover the gap between (-13/17, -sixty 9/17) and (3,-5) to get the magnificent answer.

Answer 3

The distance of a point (x_0, y_0) to a line given by the equation ax+by = c is abs(ax_0 + by_0 - c)/sqrt(a^2+b^2). [Note: my c is your -c.]
In your example, a=2, b=-3, c=4, x_0 = -1, y_0 = 4 and the distance is

abs[2*(-1)+(-3)*4-4] / sqrt(4+9) = 18/sqrt(13) = 4.99

BTW: For obvious reasons, don't omit the brackets where they are needed: sqrt(a) + b is not the same as sqrt(a+b),

Answer 4

Try A=2, B=-3, and C= -4.

To the answerer above, that equation is only for distance from a point to a point. This is the shortest distance from a point to a line, which incidentally is a perpendicular path.

Answer 5

A = 2, B=-3 , C = -4
plug in the x,y of P ; x = -1 , y =4
thus d = abs(Ax+By+c)/sqrt(A^2+B^2) = 4.99

Answer 6

your formula is incorrect plz correct it then u will get the right ans