Question

Знайдіть координати вершини В паралелограма АВСД,якщо А (-5; 3), С (6;-4), Д (-4; 6)

Answer 1

В ( 5; -7 )

решение смотр на фото

Answer 2

Finding the Coordinates of Vertex B in Parallelogram ABCD

To find the coordinates of vertex B in parallelogram ABCD, we can use the fact that opposite sides of a parallelogram are parallel and equal in length.

Given the coordinates of points A, C, and D as (-5, 3), (6, -4), and (-4, 6) respectively, we can use the midpoint formula to find the coordinates of point B.

The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:

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

Let's calculate the coordinates of vertex B using this formula:

Midpoint of AC = ((-5 + 6) / 2, (3 + (-4)) / 2) = (0.5, -0.5)

Since opposite sides of a parallelogram are parallel and equal in length, the vector connecting A to B is equal to the vector connecting C to D. We can use this information to find the coordinates of vertex B.

B = C + (Midpoint of AC - D)

Substituting the values, we get:

B = (6, -4) + (0.5, -0.5 - 6, 6) = (6, -4) + (-5.5, -6.5) = (0.5, -10.5)

Therefore, the coordinates of vertex B in parallelogram ABCD are approximately (0.5, -10.5).