Question

М-середина відрізка АВ. Знайдіть координати точки В, якщо А(1;-4),М(2;-3)

Answer 1

Xm = (Xa + Xb)/2
Xb = 2*Xm - Xa = 2*2 - 1 = 3

Ym = (Ya + Yb)/2
Yb = 2*Ym - Ya = 2*(-3) - (-4) = -6 + 4 = -2

B(3; -2)

Answer 2

Finding the coordinates of point B on the line segment AB, given A(1,-4) and M(2,-3)

To find the coordinates of point B on the line segment AB, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by the average of the x-coordinates and the average of the y-coordinates.

In this case, we have the coordinates of point A as (1, -4) and the coordinates of point M as (2, -3). We need to find the coordinates of point B, which is the midpoint of the line segment AM.

Using the midpoint formula, we can calculate the coordinates of point B as follows:

x-coordinate of B = (x-coordinate of A + x-coordinate of M) / 2 y-coordinate of B = (y-coordinate of A + y-coordinate of M) / 2

Substituting the given values, we have:

x-coordinate of B = (1 + 2) / 2 = 3 / 2 = 1.5 y-coordinate of B = (-4 + (-3)) / 2 = -7 / 2 = -3.5

Therefore, the coordinates of point B are (1.5, -3.5).

Answer: The coordinates of point B are (1.5, -3.5).