Question

rotate \\( \triangle \mathrm { alt } \\) if \\( \mathrm { a } ( - 5, - 1 ), \mathrm { l } ( - 3, - 2 ), \mathrm { t } ( - 3,2 ) \\) 90 \\( ^ { \circ } \\) clockwise about the origin, then reflect the image over the line \\( y = x \\)

Explanation:

Step1: Apply 90° clockwise rotation formula

The formula for a 90° clockwise rotation about the origin is \((x,y)\to(y, -x)\).
For \(A(-5,-1)\): \(A'=(-1,5)\)
For \(L(-3,-2)\): \(L'=(-2,3)\)
For \(T(-3,2)\): \(T'=(2,3)\)

Step2: Apply reflection over \(y = x\) formula

The formula for reflection over the line \(y=x\) is \((x,y)\to(y,x)\).
For \(A'(-1,5)\): \(A''=(5,-1)\)
For \(L'(-2,3)\): \(L''=(3,-2)\)
For \(T'(2,3)\): \(T''=(3,2)\)

Answer:

\(A'(-1,5)\), \(L'(-2,3)\), \(T'(2,3)\), \(A''(5,-1)\), \(L''(3,-2)\), \(T''(3,2)\)