Question

A (3;2) B (-1;1) 1. Записать координаты вектора AB 2. Составить уравнение прямой

Answer 1

1.   AB[(x₂-x₁),(y₂-y₁)];  x₂-x₁=-1-3=-4;  y₂-y₁=1-2=-1 ⇒ AB(-4;-1)

2.  (x-x₁)/(x₂-x₁)=(y-y₁)/(y₂-y₁)

(x-3)/(-4)=(y-2)/(-1); x-3=4y-8 ⇒ x-4y+5=0

Answer 2

To find the coordinates of the vector AB, you subtract the coordinates of point A from the coordinates of point B:

1. Coordinates of vector AB: Vector AB = (xB - xA, yB - yA) = (-1 - 3, 1 - 2) = (-4, -1)

So, the coordinates of vector AB are (-4, -1).

To find the equation of the line passing through points A and B, you can use the point-slope form of the equation of a line. The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line.

2. Equation of the line passing through A(3, 2) and B(-1, 1): First, let's find the slope (m) of the line:

m = (y2 - y1) / (x2 - x1) = (1 - 2) / (-1 - 3) = -1 / (-4) = 1/4

Now, choose either point A or B to plug into the point-slope form. Let's use point B(-1, 1):

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

Now, you can leave it in this form, or if you prefer the general form (Ax + By + C = 0) of the line equation, you can simplify it further:

4(y - 1) = x + 1 4y - 4 = x + 1 4y - x = 5

So, the equation of the line passing through points A and B is 4y - x = 5.