Question

graph the image of rhombus abcd after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Recall rotation rule

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

Step2: Identify original coordinates

Let's assume the coordinates of the vertices of rhombus $ABCD$ are $A(x_A,y_A)$, $B(x_B,y_B)$, $C(x_C,y_C)$, $D(x_D,y_D)$. From the graph, if $A(5,1)$, $B(5,6)$, $C(7,10)$, $D(7,5)$.

Step3: Apply rotation rule

For point $A(5,1)$, after rotation, $A'(- 5,-1)$.
For point $B(5,6)$, after rotation, $B'(-5,-6)$.
For point $C(7,10)$, after rotation, $C'(-7,-10)$.
For point $D(7,5)$, after rotation, $D'(-7,-5)$.

Step4: Graph new points

Plot the points $A'(-5,-1)$, $B'(-5,-6)$, $C'(-7,-10)$, $D'(-7,-5)$ and connect them to form the rotated rhombus.

Answer:

Graph the points $A'(-5,-1)$, $B'(-5,-6)$, $C'(-7,-10)$, $D'(-7,-5)$ and connect them to get the rotated rhombus.