Question

△fgh is rotated 90° counterclockwise around the origin to form △fgh.
which coordinate is the same as the
x - coordinate of point g?
x - coordinate of point g
y - coordinate of point g
opposite of x - coordinate of point g
opposite of y - coordinate of point g

Explanation:

Step1: Recall 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 transformation \((x,y)\to(-y,x)\).
For point \(G(-2,-4)\), using the formula \(x'=-y\) and \(y' = x\).

Step2: Calculate the \(x\) - coordinate of \(G'\)

For point \(G(-2,-4)\), when rotated \(90^{\circ}\) counter - clockwise around the origin.
The \(x\) - coordinate of \(G'\) is \(x'=-y\). Substituting \(y = - 4\) (the \(y\) - coordinate of \(G\)), we get \(x'=4\).

Answer:

The \(x\) - coordinate of \(G'\) is the opposite of the \(y\) - coordinate of \(G\). So the correct option is "Opposite of \(y\) - coordinate of point \(G\)".