Question

△fgh is rotated 90° counter - clockwise around the origin to form
which coordinate is the same as the
x - coordinate of point g?
opposite of y - coordinate of point g
which coordinate is the same as the
y - 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 point \((x',y')\) is given by the rule \((x,y)\to(-y,x)\).

Step2: Apply the rule to point \(G(-2,-4)\)

For point \(G(-2,-4)\), using the rotation rule \((x,y)\to(-y,x)\), we substitute \(x = - 2\) and \(y=-4\). Then \(x'=-(-4)=4\) and \(y'=-2\).

Step3: Analyze the \(y\) - coordinate of \(G'\)

The \(y\) - coordinate of \(G'\) is \(-2\). The \(x\) - coordinate of \(G\) is \(-2\). The opposite of the \(x\) - coordinate of \(G\) is \(-(-2) = 2\), the \(y\) - coordinate of \(G\) is \(-4\), the opposite of the \(y\) - coordinate of \(G\) is \(4\).

Answer:

Opposite of \(x\) - coordinate of point \(G\)