Question

the coordinates of the vertices of a quadrilateral are a(-1, -4), b(-1, -5), c(-3, -5), and d(-5, -4). quadrilateral abcd is rotated 180 - counterclockwise with the origin as the center of rotation to create quadrilateral abcd. which graph correctly shows quadrilateral abcd?

Explanation:

Step1: Recall rotation rule

The rule for a 180 - degree counter - clockwise rotation about the origin is $(x,y)\to(-x,-y)$.

Step2: Apply rule to point A

For point A$(-1,-4)$, after rotation, $x=-1,y = - 4$, so the new coordinates are $(1,4)$.

Step3: Apply rule to point B

For point B$(-1,-5)$, after rotation, $x=-1,y=-5$, so the new coordinates are $(1,5)$.

Step4: Apply rule to point C

For point C$(-3,-5)$, after rotation, $x=-3,y = - 5$, so the new coordinates are $(3,5)$.

Step5: Apply rule to point D

For point D$(-3,-4)$, after rotation, $x=-3,y=-4$, so the new coordinates are $(3,4)$.

Answer:

The graph where the vertices of the rotated quadrilateral have coordinates A$(1,4)$, B$(1,5)$, C$(3,5)$, D$(3,4)$ is the correct one. (Since no specific graph options are given in text form, the above - calculated coordinates are the key result for identifying the correct graph visually).