Question

Срочно кто поможет? Оси симметрии прямоугольника х=4,и у=3. Одна из его вершин А(7;5). Найти координаты других вершин.

Answer 1

Решение в приложении. Добавила решение аналитическое.

Answer 2

Finding the Other Vertices of the Rectangle

To find the coordinates of the other vertices of the rectangle, we can use the given information about the symmetry axes and the known vertex A(7, 5).

Given: - Symmetry axis x = 4 - Symmetry axis y = 3 - Vertex A(7, 5)

Solution:

The symmetry axes x = 4 and y = 3 divide the rectangle into four equal parts. Since A(7, 5) is in the first quadrant, the other vertices can be found by reflecting A across the symmetry axes.

Reflection across x = 4: - The x-coordinate of the reflected point will be 2 units to the left of the symmetry axis. - So, the x-coordinate of the reflected point will be 4 - (7 - 4) = 1. - The y-coordinate remains the same.

Reflection across y = 3: - The y-coordinate of the reflected point will be 2 units below the symmetry axis. - So, the y-coordinate of the reflected point will be 3 - (5 - 3) = 1. - The x-coordinate remains the same.

Calculating the Coordinates:

1. Reflection across x = 4: - New x-coordinate = 1 - Y-coordinate remains the same = 5 - So, the reflected point is B(1, 5)

2. Reflection across y = 3: - X-coordinate remains the same = 7 - New y-coordinate = 1 - So, the reflected point is C(7, 1)

3. Finding the Fourth Vertex: - The fourth vertex D can be found by reflecting A across both symmetry axes.

Reflection across x = 4: - New x-coordinate = 1 - Y-coordinate remains the same = 5 - So, the reflected point is B(1, 5)

Reflection across y = 3: - X-coordinate remains the same = 4 - New y-coordinate = 1 - So, the reflected point is D(4, 1)

Therefore, the coordinates of the other vertices of the rectangle are: - B(1, 5) - C(7, 1) - D(4, 1)