Question

7.
rotation ( 90 ^ { circ } ) clockwise
about the origin
a coordinate:
b coordinate:
c coordinate:

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) clockwise about the origin, the new coordinates \((x',y')\) are given by the rule \((x,y)\to(y, -x)\).

Step2: Find coordinates of \(A\)

The coordinates of \(A\) are \((2,0)\). Using the rule \((x,y)\to(y, -x)\), for \(x = 2\) and \(y=0\), we get \(A'(0,- 2)\).

Step3: Find coordinates of \(B\)

The coordinates of \(B\) are \((4,-2)\). Using the rule \((x,y)\to(y, -x)\), for \(x = 4\) and \(y=-2\), we substitute into the formula: \(x'=-2\) and \(y'=-4\). So \(B'(-2,-4)\).

Step4: Find coordinates of \(C\)

The coordinates of \(C\) are \((2,-4)\). Using the rule \((x,y)\to(y, -x)\), for \(x = 2\) and \(y =-4\), we substitute: \(x'=-4\) and \(y'=-2\). So \(C'(-4,-2)\).

Answer:

\(A'\) coordinate: \((0,-2)\)
\(B'\) coordinate: \((-2,-4)\)
\(C'\) coordinate: \((-4,-2)\)