Question

1. $overline{gf}$: $g(-4,5)$, $f(-3,3)$; $r_{o,-90^{circ}}circ r_{y - axis}$

Explanation:

Step1: Find the image after reflection over y - axis

The rule for reflection over the y - axis is \((x,y)\to(-x,y)\).
For point \(G(-4,5)\), after reflection over the y - axis, \(G_1(4,5)\).
For point \(F(-3,3)\), after reflection over the y - axis, \(F_1(3,3)\).

Step2: Find the image after rotation of \(- 90^{\circ}\) (which is equivalent to rotation of \(270^{\circ}\) counter - clockwise) about the origin

The rule for rotation of \((x,y)\) by \(-90^{\circ}\) (or \(270^{\circ}\) counter - clockwise) about the origin is \((x,y)\to(y,-x)\).
For point \(G_1(4,5)\), after rotation, \(G_2(5,-4)\).
For point \(F_1(3,3)\), after rotation, \(F_2(3,-3)\).

Answer:

The coordinates of the endpoints of the transformed line segment are \(G(5, - 4)\) and \(F(3,-3)\)