Question

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

Explanation:

Step1: Identify known vertices

From the graph, the horizontal segment is from \(x = 3\) (or similar) to \(x = 7\) at \(y = 4\), and the vertical segment is from \(y = 4\) to \(y = 7\) at \(x = 7\). A rectangle has opposite sides equal and parallel. So the missing vertex should have the \(x\)-coordinate of the left - most point of the horizontal segment and the \(y\)-coordinate of the top - most point of the vertical segment.
Looking at the horizontal line (red) which is at \(y = 4\) and spans from \(x = 3\) to \(x = 7\) (since the vertical line starts at \(x = 7,y = 4\) and goes up to \(y = 7\)). For a rectangle, the fourth vertex should have the same \(x\)-coordinate as the left end of the horizontal side (\(x = 3\)) and the same \(y\)-coordinate as the top end of the vertical side (\(y = 7\)).

Step2: Match with options

So the coordinates of the missing vertex should be \((3,7)\), which is option A.

Answer:

A. (3, 7)