Question

Точка К(4;-1) —середина відрізка СD. Знайдіть координати точки С, якщо D(-2;3)​

Answer 1

Нахождение координат точки К по оси абсцисс и по оси ординат:

К(х) = С(х) + D(x)/2

K(y) = C(y) + D(y)/2

Но так как у нас уже известна К, но неизвестна С, то:

С(х) = 2 × К(х) - D(x) = 2 × 4 -(-2) = 10

C(y) = 2 × K(y) -D(y) = 2 ×(-1) - 3 = -5

Ответ: (10;-5)

Answer 2

Given information:

- Point K is the midpoint of segment CD. - The coordinates of point K are (4, -1). - The coordinates of point D are (-2, 3).

Solution:

To find the coordinates of point C, we can use the midpoint formula. According to the midpoint formula, the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by:

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

In this case, we know the coordinates of point K, which is the midpoint of segment CD. We also know the coordinates of point D. Let's substitute these values into the midpoint formula and solve for the coordinates of point C.

Let's denote the coordinates of point C as (x, y).

Using the midpoint formula: K = ((x + (-2)) / 2, (y + 3) / 2)

Substituting the coordinates of point K: (4, -1) = ((x + (-2)) / 2, (y + 3) / 2)

Now, let's solve for x and y.

Multiplying both sides of the equation by 2: (8, -2) = (x + (-2), y + 3)

Simplifying: 8 = x - 2 -2 = y + 3

Adding 2 to both sides of the first equation: 8 + 2 = x - 2 + 2 10 = x

Subtracting 3 from both sides of the second equation: -2 - 3 = y + 3 - 3 -5 = y

Therefore, the coordinates of point C are (10, -5).

So, the coordinates of point C are (10, -5).