Question

think about the process suppose \\( \triangle p q r \\) is rotated \\( 270 ^ { \circ } \\) about the origin, \\( ( 0,0 ) \\). find the coordinates of \\( p ^ { \prime } \\), \\( q ^ { \prime } \\), and \\( r ^ { \prime } \\). then sketch \\( \triangle p ^ { \prime } q ^ { \prime } r ^ { \prime } \\).

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(270^{\circ}\) counter - clockwise about the origin, the transformation rule is \((x,y)\to(y, - x)\).

Step2: Find the coordinates of \(P\)

From the graph, \(P=(4,1)\). Using the rule \((x,y)\to(y, - x)\), for \(P(4,1)\), \(x = 4\) and \(y = 1\). Then \(P'=(1,-4)\).

Step3: Find the coordinates of \(Q\)

From the graph, \(Q=(8,4)\). Using the rule \((x,y)\to(y, - x)\), for \(Q(8,4)\), \(x = 8\) and \(y = 4\). Then \(Q'=(4,-8)\).

Step4: Find the coordinates of \(R\)

From the graph, \(R=(6,7)\). Using the rule \((x,y)\to(y, - x)\), for \(R(6,7)\), \(x = 6\) and \(y = 7\). Then \(R'=(7,-6)\).

Answer:

\(P'=(1,-4)\), \(Q'=(4,-8)\), \(R'=(7,-6)\)