ANSWER
Rectangle
EXPLANATION
Let us label the vertices as follows
[tex]A(1,1),B(1,4),C(5,4),D(5,1)[/tex]
The length of AB can be determined using the absolute value method because the x-values are constant.
[tex] |AB| = |4 - 1| = |3| = 3[/tex]
Also since the x-values are constant, it means it is a vertical line.
The length of BC can be determined using the absolute value method because the y-values are constant.
[tex] |BC|= |5 - 1| = |4| = 4[/tex]
This is a horizontal line.
The length of CD can be determined using the absolute value method because the x-values are constant.
[tex] |CD| = |1 - 4| = | - 3| = 3[/tex]
This is also a vertical line.
The length of AD can be determined using the absolute value method because the y-values are constant.
[tex] |AD| = |1 - 5| = | - 4| = 4[/tex]
This is a horizontal line.
Since the opposite sides are parallel and equal, the figure is a parallelogram.
