Question

1.точки В(-4:2) и D(2:-4) являются противоположными вершинами квадрата ABCD .Найдите координаты остальных вершин и координаты точки,которая делит сторону AD пополам. Желательно объясните

Answer 1

Точки B (-4;2) и D (2; -4)

Значит так, (-4;2) это же самое, что

(Х; У) , т. е. координаты В - это

значения х=-4 и у=2 у D: х=2 и у=-4.

Теперь найдем координаты на графике,

для этого чертим систему координат на

плоскости. Отложим заданные точки. В

условии написано, что это квадрат, у

квадрата все стороны равны, значит от

этих точек мы можем найти другие

противоположные координаты. Это будут:

A (-4;-4) и C (2; 2)
Координаты точки которая делит сторону AD пополам (-1; -4).

Answer 2

Finding the Coordinates of the Other Vertices of the Square ABCD

To find the coordinates of the other vertices of the square ABCD, we can use the fact that opposite sides of a square are parallel and equal in length.

Given that point B has coordinates (-4, 2) and point D has coordinates (2, -4), we can determine the length of one side of the square by calculating the distance between these two points using the distance formula:

Distance Formula: The distance between two points (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the distance between points B and D:

d = sqrt((2 - (-4))^2 + (-4 - 2)^2) = sqrt(6^2 + (-6)^2) = sqrt(36 + 36) = sqrt(72) = 6√2

Since opposite sides of a square are equal in length, the length of one side of the square is 6√2.

Now, let's find the coordinates of the other vertices of the square ABCD.

1. Point A: To find the coordinates of point A, we can move 6√2 units in the direction from point B to point D. Since the x-coordinate increases by 6 and the y-coordinate decreases by 6, the coordinates of point A are (-4 + 6√2, 2 - 6√2).

2. Point C: To find the coordinates of point C, we can move 6√2 units in the direction opposite to that from point B to point D. Since the x-coordinate decreases by 6 and the y-coordinate increases by 6, the coordinates of point C are (2 - 6√2, -4 + 6√2).

Finding the Coordinates of the Point that Divides Side AD in Half

To find the coordinates of the point that divides side AD in half, we can use the midpoint formula:

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

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

Let's find the coordinates of the midpoint of side AD, which connects point A (-4 + 6√2, 2 - 6√2) and point D (2, -4):

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

Therefore, the coordinates of the point that divides side AD in half are (-1 + 3√2, -1 - 3√2).

I hope this explanation helps! Let me know if you have any further questions.