Question

Яка з точок є серединою відрізка АВ, якщо А (3; -1; 1) ; В(1; -5; 1) а) (2; 4; 0). б) (-2; -4; 0). в) (2; -3;0)г) (4; -6; 2). д) інша відповідь​

Answer 1

Ответ:

(2;-3;1)

Объяснение:

А(3;-1;1); Ха=3; Уа=-1; Za=1

B(1;-5;1); Xв=1; Ув=-5; Zв=1

Пусть точка О будет середина отрезка АВ.

О=(А+В)/2

О(Хо;Уо;Zo)

Xo=(Xa+Xв)/2=(3+1)/2=4/2=2

Уо=(Уа+Ув)/2=(-1-5)/2=-6/2=-3

Zo=(Za+Zв)/2=(1+1)/2=2/2=1

О(2;-3;1)

Answer 2

Finding the midpoint of a line segment

To find the midpoint of a line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1, z1) and (x2, y2, z2) are given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

Let's calculate the midpoint for each given set of points.

a) A(3, -1, 1) and B(1, -5, 1)

Using the midpoint formula, we can calculate the midpoint as follows:

Midpoint = ((3 + 1)/2, (-1 + -5)/2, (1 + 1)/2) = (2, -3, 1)

Therefore, the midpoint of the line segment AB, where A(3, -1, 1) and B(1, -5, 1), is (2, -3, 1).

b) A(3, -1, 1) and B(-2, -4, 0)

Using the midpoint formula, we can calculate the midpoint as follows:

Midpoint = ((3 + -2)/2, (-1 + -4)/2, (1 + 0)/2) = (0.5, -2.5, 0.5)

Therefore, the midpoint of the line segment AB, where A(3, -1, 1) and B(-2, -4, 0), is (0.5, -2.5, 0.5).

c) A(3, -1, 1) and B(2, 4, 0)

Using the midpoint formula, we can calculate the midpoint as follows:

Midpoint = ((3 + 2)/2, (-1 + 4)/2, (1 + 0)/2) = (2.5, 1.5, 0.5)

Therefore, the midpoint of the line segment AB, where A(3, -1, 1) and B(2, 4, 0), is (2.5, 1.5, 0.5).

d) A(3, -1, 1) and B(4, -6, 2)

Using the midpoint formula, we can calculate the midpoint as follows:

Midpoint = ((3 + 4)/2, (-1 + -6)/2, (1 + 2)/2) = (3.5, -3.5, 1.5)

Therefore, the midpoint of the line segment AB, where A(3, -1, 1) and B(4, -6, 2), is (3.5, -3.5, 1.5).

Conclusion

To summarize, the midpoints of the given line segments are as follows: a) (2, -3, 1) b) (0.5, -2.5, 0.5) c) (2.5, 1.5, 0.5) d) (3.5, -3.5, 1.5)

Please let me know if there's anything else I can help you with!