Question

Помогиитеее пожалуйста отметке на кооординатной плоскости точки М(0;5)N(8;1)C(2;2) D(-6;-2) найдите координаты точки пересечения прямых MN и CD .на какой из этих прямых лежит точка К(0;1)?

Answer 1

Построй точки на координатной плоскости и найди координаты точки пересечения, опустив перпендикуляры на ось ОХ и ось ОУ.

Координаты точки пересечения прямых MN и CD: (4; 3).
Точка К (0;1) лежит на прямой CD.
Вроде так....И да там вместо B кажется D

Answer 2

Finding the Intersection Point of Lines MN and CD

To find the coordinates of the intersection point of lines MN and CD, we can use the slope-intercept form of a linear equation. The slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

Let's find the equations of lines MN and CD first:

Line MN passes through points M(0,5) and N(8,1). To find the slope of MN, we can use the formula m = (y2 - y1) / (x2 - x1). Substituting the coordinates of M and N, we have:

m(MN) = (1 - 5) / (8 - 0) = -4 / 8 = -1/2

The equation of line MN can be written as y = (-1/2)x + b. To find the value of b, we can substitute the coordinates of point M into the equation:

5 = (-1/2)(0) + b

Simplifying, we find b = 5.

Therefore, the equation of line MN is y = (-1/2)x + 5.

Line CD passes through points C(2,2) and D(-6,-2). Using the same process, we can find the equation of line CD:

m(CD) = (-2 - 2) / (-6 - 2) = -4 / -8 = 1/2

Substituting the coordinates of C and D, we find b = 1.

Therefore, the equation of line CD is y = (1/2)x + 1.

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

(-1/2)x + 5 = (1/2)x + 1

Simplifying, we have x = 4.

Substituting this value of x into either equation, we can find the corresponding y coordinate:

y = (-1/2)(4) + 5 = 3

Therefore, the intersection point of lines MN and CD is (4,3).

Determining if Point K Lies on Either Line

To determine if point K(0,1) lies on either line MN or CD, we can substitute the coordinates of K into the equations of the lines and check if the equations hold true.

For line MN:

1 = (-1/2)(0) + 5 1 = 5

The equation does not hold true, so point K does not lie on line MN.

For line CD:

1 = (1/2)(0) + 1 1 = 1

The equation holds true, so point K lies on line CD.

Therefore, point K(0,1) lies on line CD.