Question

quinton tried to transform triangle fgh according to the rule ((x, y) \to (-y, x)). which best describes his attempt?

• correct. he transformed the triangle according to the rule ((x, y) \to (-y, x)).
• incorrect. he transformed the triangle according to the rule ((x, y) \to (y, -x))
• incorrect. he transformed the triangle according to the rule ((x, y) \to (-y, -x))
• incorrect. he transformed the triangle according to the rule ((x, y) \to (-x, -y))

Explanation:

Step1: Identify original triangle vertices

Let's take vertices of triangle FGH:
Assume original vertices (from graph):
$F(2,1)$, $G(4,1)$, $H(4,5)$

Step2: Apply target rule $(-y,x)$

Calculate transformed points for target rule:
For $F(2,1)$: $(-1, 2)$
For $G(4,1)$: $(-1, 4)$
For $H(4,5)$: $(-5, 4)$

Step3: Identify actual transformed vertices

From graph, the transformed triangle vertices are:
$F'(-2,-1)$, $G'(-4,-1)$, $H'(-4,-5)$

Step4: Match actual transformation rule

Compare original and actual transformed points:
For $F(2,1)\to(-2,-1)$: $(x,y)\to(-x,-y)$
For $G(4,1)\to(-4,-1)$: $(x,y)\to(-x,-y)$
For $H(4,5)\to(-4,-5)$: $(x,y)\to(-x,-y)$
This matches the fourth option's rule.

Answer:

Incorrect. He transformed the triangle according to the rule $(x, y) \to (-x, -y)$