Question

. Побудуйте відрізки АВ і СD та знайдіть координати точки перетину цих відрізків, якщо А (-1; -3 ), В (3; 1), С (0; 4), D (3; -2). ПОМОГИТЕ СРОЧНО ПОЖАЛУЙСТА

Answer 1

Ответ: (2;0)

Пошаговое объяснение:

Answer 2

Finding the Lengths of AB and CD

To find the lengths of AB and CD, we can use the distance formula, which states that 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 lengths of AB and CD using this formula:

For AB: - Point A: (-1, -3) - Point B: (3, 1)

Using the distance formula, we can calculate the length of AB as follows:

d_AB = sqrt((3 - (-1))^2 + (1 - (-3))^2)

Simplifying the equation: d_AB = sqrt(4^2 + 4^2) = sqrt(16 + 16) = sqrt(32) = 4 * sqrt(2)

For CD: - Point C: (0, 4) - Point D: (3, -2)

Using the distance formula, we can calculate the length of CD as follows:

d_CD = sqrt((3 - 0)^2 + (-2 - 4)^2)

Simplifying the equation: d_CD = sqrt(3^2 + (-6)^2) = sqrt(9 + 36) = sqrt(45) = 3 * sqrt(5)

Therefore, the length of AB is 4 * sqrt(2) and the length of CD is 3 * sqrt(5).

Finding the Intersection Point of AB and CD

To find the intersection point of AB and CD, we can set up the equations of the lines AB and CD and solve them simultaneously.

The equation of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

y - y1 = ((y2 - y1) / (x2 - x1)) * (x - x1)

Let's set up the equations for AB and CD:

For AB: - Point A: (-1, -3) - Point B: (3, 1)

The equation of AB is: y - (-3) = ((1 - (-3)) / (3 - (-1))) * (x - (-1))

Simplifying the equation: y + 3 = (4 / 4) * (x + 1) y + 3 = x + 1 y = x - 2

For CD: - Point C: (0, 4) - Point D: (3, -2)

The equation of CD is: y - 4 = ((-2 - 4) / (3 - 0)) * (x - 0)

Simplifying the equation: y - 4 = (-6 / 3) * x y - 4 = -2x y = -2x + 4

Now, we can solve these two equations simultaneously to find the intersection point.

Substituting the equation of AB into the equation of CD: x - 2 = -2x + 4

Simplifying the equation: 3x = 6 x = 2

Substituting the value of x back into the equation of AB: y = 2 - 2 = 0

Therefore, the intersection point of AB and CD is (2, 0).

To summarize: - The length of AB is 4 * sqrt(2). - The length of CD is 3 * sqrt(5). - The intersection point of AB and CD is (2, 0).

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