Question

Даны 2 точки. А(7;-3),В(23;-6). Найти координаты точки пересечения с осью Ох.

Answer 1

Найдем уравнение прямой АВ. Ищем в виде: у = kx+b. Подставим в это уравнение координаты данных точек А и В и найдем k и b:

7k + b = -3,

23k + b =-6,   вычтем и получим: 16k = -3,    k = -3/16

Тогда: b = -3-7k = -3 + 21/16  =  -27/16

Прямая АВ имеет уравнение: у = -3х/16 - 27/16

Приравняем у 0 и найдем координату пересечения прямой с ОХ:

-3х/16  -  27/16  =  0

-3х = 27

х = -9

Координаты точки пересечения с ОХ:   (-9; 0)

Answer 2

Finding the Intersection Point with the X-Axis

To find the coordinates of the point of intersection with the x-axis, we can use the given points A(7, -3) and B(23, -6).

The x-axis is where the y-coordinate is 0. Therefore, to find the point of intersection with the x-axis, we need to find the x-coordinate when y = 0.

First, let's find the equation of the line passing through points A and B using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

For points A(7, -3) and B(23, -6): m = (-6 - (-3)) / (23 - 7) = (-6 + 3) / (23 - 7) = -3 / 16.

Now that we have the slope, we can find the y-intercept (b) using point A(7, -3) and the slope (m).

Let's calculate the y-intercept (b) and then find the equation of the line passing through points A and B.

The equation of the line passing through points A and B is y = -0.1875x - 4.3125.

Now, we can find the x-coordinate when y = 0 to determine the point of intersection with the x-axis.

Let's calculate the x-coordinate for y = 0 using the equation of the line.

The x-coordinate for y = 0 is x = 23.

Therefore, the coordinates of the point of intersection with the x-axis are (23, 0).

Summary

The coordinates of the point of intersection with the x-axis are (23, 0).