Which is the equation of the line that passes through the points A(1;2) and B(-1;-2)

Expert Answers
hala718 eNotes educator| Certified Educator

We hav the points: A(1, 2) and B(-1,-2)

The equation for the line passes through the points is:

y-yA = m(x-xA)  where m is the slope:

m = (yB-yA)/(xB-xA)

   = -2-2/ -1-1 = -4/-2 = 2

==> y- 2 = 2( x-1)

==> y-2 = 2x -2

==> y = 2x -2 + 2

==>  y = 2x

neela | Student

To find the equation of the line passing through A(1,2) and B((-1,-2).

Solution:

The equation of the line passing through any two points (x1,y1) and (x2,y2) is

(y-y1) = [(y2-y1)/(x2-x1)}(x-x1)............(1)

Here  (x1,y1) = (1,2) and (x2,y2) = (-1,-2). Substitute in (1):

y-2 = {(-2-2)/(-1-1)}(x-1)

y-2 = 2(x-1)

y-2 =2x-1

2x-y-1+2 = 0

2x-y-1 = 0 is the line.

giorgiana1976 | Student

To determine the equation of the line AB, we'll write the formula:

(xB-xA)/(x-xA) = (yB-yA)/(y-yA)

Now, we'll substitute the coordinates of the points A and B, into the formula above:

(-1-1)/(x-1) = (-2-2)/(y-2)

-2/(x-1) = -4/(y-2)

We'll divide by -2 both sides:

1/(x-1) = 2/(y-2)

We'll cross multiply:

2x - 2 = y - 2

We'll eliminate like terms:

y = 2x

So, the equation of the line AB is: y = 2x