Question

. В координатной плоскости через точки A(–1; –1) и В(–2; 4) проведена прямая AB, через точки L(6; 0) и N(4; 2) проведена прямая LN. Найди координаты точки пересечения прямой AB и прямой LN. помогите пожалуйста срочно надо ​

Answer 1

Ответ:

(-3;9)

Пошаговое объяснение:

см. файл

Answer 2

Finding the Intersection Point of Two Lines

To find the intersection point of the lines AB and LN, we can use the equations of the lines. The line AB passes through points A(-1, -1) and B(-2, 4), while the line LN passes through points L(6, 0) and N(4, 2).

Let's find the equations of the lines AB and LN first.

Equation of Line AB

The equation of a line can be expressed in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of line AB, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

For line AB, the coordinates are A(-1, -1) and B(-2, 4).

m_AB = (4 - (-1)) / (-2 - (-1)) = 5 / (-1) = -5

Now, we can use the point-slope form of the equation to find the equation of line AB. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Using point A(-1, -1):

y - (-1) = -5(x - (-1)) y + 1 = -5(x + 1) y + 1 = -5x - 5 y = -5x - 6

So, the equation of line AB is y = -5x - 6.

Equation of Line LN

Using the same process, we can find the equation of line LN.

For line LN, the coordinates are L(6, 0) and N(4, 2).

m_LN = (2 - 0) / (4 - 6) = 2 / (-2) = -1

Using point L(6, 0):

y - 0 = -1(x - 6) y = -x + 6

So, the equation of line LN is y = -x + 6.

Finding the Intersection Point

To find the intersection point, we can set the equations of the two lines equal to each other and solve for x and y.

-5x - 6 = -x + 6

Simplifying the equation:

-5x + x = 6 + 6 -4x = 12 x = -3

Substituting the value of x into either equation, let's use y = -5x - 6:

y = -5(-3) - 6 y = 15 - 6 y = 9

Therefore, the coordinates of the intersection point of line AB and line LN are (-3, 9).

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