Question

directions: select all the correct locations on the coordinate plane. triangle abc is defined by points a(-3,1), b(1,4), and c(-2,-2). if the triangle is rotated counterclockwise 90° about the origin, then translated up 2 units, and then reflected about the y - axis, determine the locations of a, b, and c, the vertices of the resulting triangle.

Explanation:

Step1: Rotate counter - clockwise 90°

The rule for a counter - clockwise rotation of 90° about the origin is \((x,y)\to(-y,x)\).
For point \(A(-3,1)\): \((-3,1)\to(-1,-3)\)
For point \(B(1,4)\): \((1,4)\to(-4,1)\)
For point \(C(-2,-2)\): \((-2,-2)\to(2,-2)\)

Step2: Translate up 2 units

The rule for a translation up 2 units is \((x,y)\to(x,y + 2)\).
For \((-1,-3)\): \((-1,-3)\to(-1,-1)\)
For \((-4,1)\): \((-4,1)\to(-4,3)\)
For \((2,-2)\): \((2,-2)\to(2,0)\)

Step3: Reflect about the \(y\) - axis

The rule for a reflection about the \(y\) - axis is \((x,y)\to(-x,y)\).
For \((-1,-1)\): \((-1,-1)\to(1,-1)\)
For \((-4,3)\): \((-4,3)\to(4,3)\)
For \((2,0)\): \((2,0)\to(-2,0)\)

Answer:

\(A'(1,-1)\), \(B'(4,3)\), \(C'(-2,0)\)