The vertices of the parallelogram in the rectangular coordinate system xOy lie at the points

| September 3, 2021 | education

The vertices of the parallelogram in the rectangular coordinate system xOy lie at the points A (4.0), B (6.5), C (2.5), O (0.0). Find its area.

1. The area of the parallelogram is equal to the product of the side of the parallelogram by the height lowered to this side:
S = a * h = OA * h.
2. Find the length of the segment OA:
| ОА | = √ ((y2-y1) ² + (x2-x1) ²) = √ ((0-4) ² + (0-0) ²) = 4 cm.
3. Find the height:
The height of CH is perpendicular to the base, which means it is parallel to the Y axis, which means that the point of intersection with the base has coordinates along Y = 0, and along OX the coordinate of the point C x = 2, H (2,0), we find the length of CH:
| CH | = √ ((y2-y1) ² + (x2-x1) ²) = √ ((2-2) ² + (5-0) ²) = 5 cm.
4. Find the area:
S = a * h = OA * h = 4 * 5 = 20 cm².
Answer: the area of the parallelogram is 20 cm.



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