Question

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Explanation:

Part a)

Step1: Determine coordinates of A

From the graph, A is at (0, 3) (assuming each grid is 1 unit, x=0, y=3).

Step2: Determine coordinates of B

B is at (2, 1) (x=2, y=1).

Step3: Determine coordinates of C

C is at (-2, 2) (x=-2, y=2).

A \( 180^\circ \) clockwise (or counter - clockwise, since \( 180^\circ \) rotation is the same in both directions) rotation about the origin has the rule that for a point \((x,y)\), the image after rotation is \((-x,-y)\). This is because rotating a point \( 180^\circ \) around the origin means that both the x - coordinate and y - coordinate are negated.

Step1: Find \( A' \)

For point A(0, 3), using the rule \((x,y)\to(-x,-y)\), substitute \( x = 0\) and \( y=3\). We get \( A'(-0,-3)=(0, - 3)\).

Step2: Find \( B' \)

For point B(2, 1), substitute \( x = 2\) and \( y = 1\) into the rule \((x,y)\to(-x,-y)\). We get \( B'(-2,-1)\).

Step3: Find \( C' \)

For point C(-2, 2), substitute \( x=-2\) and \( y = 2\) into the rule \((x,y)\to(-x,-y)\). We get \( C'(2,-2)\).

Answer:

A: (0, 3), B: (2, 1), C: (-2, 2)

Part b)