Question

A student designed a flag for the school's Gaming Club. The design is rectangular with vertices at (3, 7), (11, −9), and (3, −9). Find the missing vertex and the area of the flag in square inches?

The missing vertex is (−9, 7) with an area of 16 in2.
The missing vertex is (7, 11) with an area of 16 in2.
The missing vertex is (−9, 11) with an area of 128 in2.
The missing vertex is (11, 7) with an area of 128 in2.

Answer 1

(11, 7) with an area of 128 in2.

Explanation:

Answer 2

The missing vertex is (11, 7) with an area of 128 in2.

To find the missing vertex, we can use the fact that opposite sides of a rectangle are parallel and have the same length. The length of the side connecting (3, 7) and (3, -9) is 16 units, so the length of the side connecting (11, -9) and the missing vertex must also be 16 units. This means that the missing vertex must be at (11, 7).

To find the area of the rectangle, we can use the length and width of the rectangle, which are the distances between the corresponding vertices. The length is the distance between (3, 7) and (11, 7), which is 8 units. The width is the distance between (3, 7) and (3, -9), which is 16 units. Therefore, the area is length times width, which is 8 times 16, or 128 square inches.

Therefore, the answer is the missing vertex is (11, 7) with an area of 128 in2.