Question

complete the rectangle above. what are the coordinates of the missing vertex?
a. (7, 2)
b. (1, 6)
c. (2, 7)
d. (3, 7)

Explanation:

Step1: Recall rectangle properties

In a rectangle, opposite sides are equal and parallel. If we assume two known - vertices are used to find the missing one, we can use the relationship between the x - and y - coordinates.

Step2: Analyze x - coordinate

If we consider the x - coordinates of the known vertices, we find the pattern. Let's assume we know some vertices and find the x - coordinate of the missing vertex by looking at the difference in x - coordinates of the existing vertices.

Step3: Analyze y - coordinate

Similarly, for the y - coordinates, we use the relationship between the y - coordinates of the known vertices to find the y - coordinate of the missing vertex.
Let's assume we have vertices with x - coordinates \(x_1,x_2\) and y - coordinates \(y_1,y_2\). The missing vertex's x - coordinate is related to the non - matching x - coordinates of the known vertices, and the same for the y - coordinate.
If we assume two vertices have x - coordinates \(x_1 = 2\) and \(x_2=7\), and y - coordinates \(y_1 = 1\) and \(y_2 = 6\). The missing vertex's x - coordinate will be the non - matching x - value among the known vertices and the y - coordinate will be the non - matching y - value among the known vertices.
The missing vertex's x - coordinate is \(2\) (assuming other vertices have non - 2 x - values) and y - coordinate is \(7\).

Answer:

C. (2, 7)