Question

rectangles have four right angles and opposite sides that are parallel.
a. is the figure shown a rectangle? explain.
b. if not, how could the points change so it would be a rectangle?
b. select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice
a. to make the figure a rectangle, change point c to (□, - 4).
b. to make the figure a rectangle, change point d to (□, 1).
c. to make the figure a rectangle, change point c to (□, - 4) and point d to (□, 1).
d. the figure shown is a rectangle.

Explanation:

Step1: Determine if the figure is a rectangle

A rectangle has four right angles and opposite sides parallel. By observing the figure (assuming standard grid - based analysis of slopes for parallelism and right - angle checks), we can see that it is not a rectangle.

Step2: Analyze the coordinates for transformation

For a rectangle, if we assume the x - coordinate of point \(A\) is \(1\) and \(y = 2\), point \(B\) has \(x=6\) and \(y = 2\). For a rectangle, if we consider the vertical and horizontal alignments. If we want to make it a rectangle, by using the properties of rectangles (equal and parallel opposite sides), we find that changing point \(C\) to \((6,-4)\) and point \(D\) to \((1,1)\) will satisfy the rectangle properties.

Answer:

C. To make the figure a rectangle, change point \(C\) to \((6,-4)\) and point \(D\) to \((1,1)\)