Question

what is the fourth vertex of the rectangle with vertices at (1,4), (1,-4) and (-5,-4)?

Explanation:

Step1: Analyze the x - coordinates

In a rectangle, opposite sides are equal. The x - coordinates of two given points \((1,4)\) and \((1, - 4)\) are the same (\(x = 1\)). The x - coordinate of the third point is \(x=-5\). For the rectangle, the fourth point's x - coordinate should be the same as the x - coordinate of the point that is opposite in the rectangle. Since one pair of points has \(x = 1\) and the other has \(x=-5\), we need to find the x - coordinate for the fourth vertex.

Step2: Analyze the y - coordinates

The y - coordinates of \((1,-4)\) and \((-5,-4)\) are the same (\(y=-4\)). The y - coordinate of the first point is \(y = 4\). For the rectangle, the fourth point's y - coordinate should be the same as the y - coordinate of the point that is opposite in the rectangle.

Combining the x - coordinate from the non - matching x - value pair (\(x=-5\)) and the y - coordinate from the non - matching y - value pair (\(y = 4\))

Answer:

\((-5,4)\)