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 point \((x',y')\) has the transformation rule \((x,y)\to(-y,x)\).

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

For point \(G(-2,-4)\), using the \(90^{\circ}\) counter - clockwise rotation rule \((x,y)\to(-y,x)\). Here \(x = - 2\) and \(y=-4\). Then \(x'=-y=-(-4) = 4\) and \(y'=x=-2\). So \(G'=(4,-2)\)

Step3: Compare the coordinates

The \(x\) - coordinate of \(G'\) is \(4\). The \(y\) - coordinate of \(G\) is \(-4\), and its opposite is \(4\).

Answer:

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