Question

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$\triangle fgh$ is rotated $90^{circ}$ counterclockwise around the origin to form $\triangle fgh$.
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 coordinates \((x',y')\) are 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 \((x,y)\to(-y,x)\). Here \(x = - 2\) and \(y=-4\). Then \(x'=-y=-(-4) = 4\) and \(y'=x=-2\).

Answer:

The \(x\) - coordinate of \(G'\) is the opposite of the \(y\) - coordinate of \(G\). The \(y\) - coordinate of \(G'\) is the \(x\) - coordinate of \(G\).