Question

Срочноооооо!!!!помогите.Даю 20 баллов!!!! Дані координати трьох вершин прямокутника АВСD: А(–4; –2), C(2; 4), D(2; –2). Накресліть цей прямокутник; Знайдіть координати точки B; Знайдіть координати точки перетину діагоналей; Знайдіть координати середин сторін прямокутника; Обчисліть площу та периметр прямокутника, вважаючи що довжина одиничного відрізка дорівнює 1 см​

Answer 1

Ответ:

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Answer 2

Drawing the Rectangle

To draw the rectangle ABCD with the given coordinates, we can plot the points on a coordinate plane and connect them with straight lines. Here is the rectangle:

A(-4, -2)     B(2, -2)

D(-4, 4)      C(2, 4)

Finding the Coordinates of Point B

To find the coordinates of point B, we can observe that point B has the same y-coordinate as point A and the same x-coordinate as point C. Therefore, the coordinates of point B are (2, -2).

Finding the Coordinates of the Intersection of Diagonals

To find the coordinates of the intersection of the diagonals, we can calculate the midpoint of the line segment AC and the midpoint of the line segment BD. The intersection point will be the same for both.

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the following formulas: - Midpoint x-coordinate = (x1 + x2) / 2 - Midpoint y-coordinate = (y1 + y2) / 2

Using these formulas, we can find the midpoint of AC and BD:

Midpoint of AC: - x-coordinate = (-4 + 2) / 2 = -1 - y-coordinate = (-2 + 4) / 2 = 1

Midpoint of BD: - x-coordinate = (-4 + 2) / 2 = -1 - y-coordinate = (4 + -2) / 2 = 1

Therefore, the coordinates of the intersection of the diagonals are (-1, 1).

Finding the Coordinates of the Midpoints of the Sides

To find the coordinates of the midpoints of the sides of the rectangle, we can use the midpoint formula mentioned earlier.

Midpoint of AB: - x-coordinate = (-4 + 2) / 2 = -1 - y-coordinate = (-2 + -2) / 2 = -2

Midpoint of BC: - x-coordinate = (2 + 2) / 2 = 2 - y-coordinate = (-2 + 4) / 2 = 1

Midpoint of CD: - x-coordinate = (-4 + 2) / 2 = -1 - y-coordinate = (4 + -2) / 2 = 1

Midpoint of AD: - x-coordinate = (-4 + -4) / 2 = -4 - y-coordinate = (-2 + 4) / 2 = 1

Therefore, the coordinates of the midpoints of the sides of the rectangle are: - Midpoint of AB: (-1, -2) - Midpoint of BC: (2, 1) - Midpoint of CD: (-1, 1) - Midpoint of AD: (-4, 1)

Calculating the Area and Perimeter of the Rectangle

To calculate the area of the rectangle, we can use the formula: Area = length × width. In this case, the length is the distance between points A and D, and the width is the distance between points A and B.

Using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2), we can calculate the distances:

Distance between A and D: - x2 - x1 = 2 - (-4) = 6 - y2 - y1 = -2 - 4 = -6 - Distance = √(6^2 + (-6)^2) = √(36 + 36) = √72 ≈ 8.49 cm

Distance between A and B: - x2 - x1 = 2 - (-4) = 6 - y2 - y1 = -2 - (-2) = 0 - Distance = √(6^2 + 0^2) = √36 = 6 cm

Therefore, the area of the rectangle is approximately 8.49 cm × 6 cm = 50.94 cm².

To calculate the perimeter of the rectangle, we can use the formula: Perimeter = 2 × (length + width). In this case, the length is the distance between points A and D, and the width is the distance between points A and B.

Using the distances calculated earlier:

Perimeter = 2 × (8.49 cm + 6 cm) = 2 × 14.49 cm ≈ 28.98 cm

Therefore, the perimeter of the rectangle is approximately 28.98 cm.

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