Question

triangle abc is reflected across the line y = x. the result is △abc, as shown below. (a) the arrows below show that the coordinates on the left are mapped to the coordinates on the right. fill in the blanks to give the coordinates after the reflection. original coordinates → final coordinates a(-3,8)→a(, ) b(2,5)→b(, ) c(-4,-1)→c(, ) (b) choose the general rule below that describes the reflection mapping △abc to △abc. (x,y)→(-y,x) (x,y)→(-x,y) (x,y)→(y,x) (x,y)→(-y,-x) (x,y)→(y,-x) (x,y)→(-x,-y) (x,y)→(x,-y)

Explanation:

Step1: Recall the rule for reflection over the line \(y = x\)

When a point \((x,y)\) is reflected over the line \(y=x\), the rule is \((x,y)\to(y,x)\).

Step2: Apply the rule to point \(A(-3,8)\)

For \(A(-3,8)\), swap \(x=-3\) and \(y = 8\). So \(A'=(8,-3)\).

Step3: Apply the rule to point \(B(2,5)\)

For \(B(2,5)\), swap \(x = 2\) and \(y=5\). So \(B'=(5,2)\).

Step4: Apply the rule to point \(C(-4,-1)\)

For \(C(-4,-1)\), swap \(x=-4\) and \(y=-1\). So \(C'=(-1,-4)\).

Step5: Identify the general rule

Since the transformation is \((x,y)\to(y,x)\) (from the reflection over \(y = x\) rule).

Answer:

(a) \(A(-3,8)\to A'(8, - 3)\), \(B(2,5)\to B'(5,2)\), \(C(-4,-1)\to C'(-1,-4)\)
(b) \((x,y)\to(y,x)\)