Question

Точка А ділить відрізок МК у відношенні 3 : 1. Знайти координати точки А, якщо М (–7; 6), К (5; –2)

Answer 1

Ответ:

(2;0)

Объяснение:

Answer 2

Finding the Coordinates of Point A

To find the coordinates of point A, given that point M has coordinates (-7, 6) and point K has coordinates (5, -2), we can use the concept of dividing a line segment in a given ratio.

The coordinates of point A can be found using the following formula: A(x, y) = ((x1 + rx2) / (1 + r), (y1 + ry2) / (1 + r))

Where: - (x1, y1) = Coordinates of point M - (x2, y2) = Coordinates of point K - r = Ratio in which the line segment MK is divided

In this case, the ratio is given as 3:1.

Calculating the Coordinates of Point A

Using the given coordinates of points M and K, and the ratio 3:1, we can calculate the coordinates of point A as follows:

x-coordinate of A: ((x1 + 3x2) / (3 + 1)) = ((-7 + 3*5) / 4) = (8 / 4) = 2

y-coordinate of A: ((y1 + 3y2) / (3 + 1)) = ((6 + 3*(-2)) / 4) = (0 / 4) = 0

Conclusion

Therefore, the coordinates of point A are (2, 0).