Question

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?
opposite of x - coordinate of point g
x - coordinate of point g
y - coordinate of point g
g(-2, -4)
g(4, -2)

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise around the origin, the new coordinates \((x',y')\) follow the rule \((x,y)\to(-y,x)\). For point \(G(-2, - 4)\), after rotation, \(G'=(4,-2)\).

Step2: Compare coordinates

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

Answer:

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