Question

design fiona is using graphic design software to make stickers. to create the final shape of her design, she combines the image and preimage of a triangle. she graphs the triangle on a coordinate plane with vertices at p(0, 4), q(2, 8), and r(-3, 6). then she draws a reflection of the triangle, and the vertices of the image are at p(0, 4), q(-2, 8), and r(3, 6). draw the preimage and image of the triangle on a separate sheet of paper. describe the transformation. use decimals, if necessary. (x, y) → ( )( )

Explanation:

Step1: Analyze x - coordinates

Pre - image points: \(P(0,4)\), \(Q(2,8)\), \(R(-3,6)\); Image points: \(P'(0,4)\), \(Q'(-2,8)\), \(R'(3,6)\). For point \(Q\) with \(x = 2\) in pre - image and \(x=-2\) in image, for point \(R\) with \(x = - 3\) in pre - image and \(x = 3\) in image. The \(x\) - coordinate of each point is multiplied by \(-1\) while the \(y\) - coordinate remains the same.

Step2: Write the transformation rule

The general rule for a point \((x,y)\) in the pre - image to a point \((x',y')\) in the image is \((x,y)\to(-x,y)\)

Answer:

\(-x,y\)