Question

graph the image of kite qrst 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

Assume the coordinates of the vertices of kite $QRST$ are $Q(x_Q,y_Q)$, $R(x_R,y_R)$, $S(x_S,y_S)$, $T(x_T,y_T)$. For example, if $Q(- 5,-8)$, $R(-2,-3)$, $S(-5,1)$, $T(-8,-3)$.

Step3: Apply rotation rule

For point $Q(-5,-8)$, the new coordinates $Q'$ are $(5,8)$. For point $R(-2,-3)$, the new coordinates $R'$ are $(2,3)$. For point $S(-5,1)$, the new coordinates $S'$ are $(5,-1)$. For point $T(-8,-3)$, the new coordinates $T'$ are $(8,3)$.

Step4: Graph new points

Plot the new points $Q'$, $R'$, $S'$, $T'$ on the same coordinate grid and connect them to form the rotated kite.

Answer:

Graph the new kite with vertices obtained by applying the $(x,y)\to(-x,-y)$ rule to the original vertices of kite $QRST$.