Question

the coordinates of the vertices of \\( \triangle fgh \\) are \\( f(-4,1) \\), \\( g(-3,-2) \\), and \\( h(-5,5) \\)
the coordinates of the vertices of \\( \triangle fgh \\) are \\( f(4,4) \\), \\( g(3,1) \\), and \\( h(5,8) \\)
drag and drop the answers into the boxes to correctly complete the statement
a sequence of transformations that maps \\( \triangle fgh \\) to \\( \triangle fgh \\) is a
followed by a
rotation of \\( 180^{\circ} \\) about the origin translation 3 units up translation 3 units left
reflection across the \\( y \\)-axis

Explanation:

Step1: Analyze reflection across the y - axis

The rule for reflection across the y - axis is \((x,y)\to(-x,y)\).
For point \(F(-4,1)\), after reflection across the y - axis, it becomes \((4,1)\). For point \(G(-3,-2)\), it becomes \((3,-2)\). For point \(H(-5,5)\), it becomes \((5,5)\).

Step2: Analyze translation

The rule for translation \(3\) units up is \((x,y)\to(x,y + 3)\).
For the point \((4,1)\) after translation \(3\) units up, it becomes \((4,1+3)=(4,4)\). For the point \((3,-2)\) after translation \(3\) units up, it becomes \((3,-2 + 3)=(3,1)\). For the point \((5,5)\) after translation \(3\) units up, it becomes \((5,5+3)=(5,8)\).

Answer:

A sequence of transformations that maps \(\triangle FGH\) to \(\triangle F'G'H'\) is a reflection across the \(y\) - axis followed by a translation \(3\) units up.