Question

△fgh is rotated 90° counterclockwise around the origin to form △fgh.
what are the coordinates of point g
and point g?
g(?,?)
g(?,?)

Explanation:

Step1: Determine the coordinates of point G

From the graph, we can observe that point G is located at \((-1,-4)\).

Step2: Apply the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise around the origin, the new coordinates \((x',y')\) are given by the rule \((x,y)\to(-y,x)\).
For point \(G(-1,-4)\), substituting \(x = - 1\) and \(y=-4\) into the rule:
\(x'=-(-4) = 4\) and \(y'=-1\). So the coordinates of \(G'\) are \((4,-1)\).

Answer:

\(G(-1,-4)\), \(G'(4,-1)\)