Question

Найти точку пересечения высот треугольника АВС координаты вершин треугольника: A (-4: 0) B (-2; -2) C (2; 2) максимально подробно

Answer 1

0622вот правильный ответ

Answer 2

Finding the Intersection Point of the Altitudes of Triangle ABC

To find the intersection point of the altitudes of triangle ABC with the given coordinates of its vertices A(-4, 0), B(-2, -2), and C(2, 2), we can follow these steps:

1. Find the Slopes of the Sides of the Triangle: - The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: \[ m = \frac{y2 - y1}{x2 - x1} \] - We can use this formula to find the slopes of the sides AB, BC, and AC.

2. Find the Equations of the Altitudes: - The equation of a line passing through a point (x1, y1) with slope m is given by: \[ y - y1 = m(x - x1) \] - We can use this equation to find the equations of the altitudes from each vertex.

3. Solve for the Intersection Point: - Once we have the equations of the altitudes, we can solve them simultaneously to find the intersection point.

Let's proceed with these steps to find the intersection point of the altitudes of triangle ABC.

Step 1: Finding the Slopes of the Sides of the Triangle

The slopes of the sides AB, BC, and AC can be calculated using the given coordinates of the vertices.

The slope of AB: \[ m_{AB} = \frac{-2 - 0}{-2 - (-4)} = \frac{-2}{2} = -1 \]

The slope of BC: \[ m_{BC} = \frac{2 - (-2)}{2 - (-2)} = \frac{4}{4} = 1 \]

The slope of AC: \[ m_{AC} = \frac{2 - 0}{2 - (-4)} = \frac{2}{6} = \frac{1}{3} \]

Step 2: Finding the Equations of the Altitudes

We can use the slopes we found to determine the equations of the altitudes from each vertex.

For example, the equation of the altitude from vertex A can be found using the point-slope form with the slope \( m_{AB} \) and the coordinates of A (-4, 0).

Step 3: Solving for the Intersection Point

After obtaining the equations of the altitudes, we can solve them simultaneously to find the intersection point.

Let's proceed with these calculations to find the exact coordinates of the intersection point of the altitudes of triangle ABC.