Question

critical thinking the blue figure is a transformation of the red figure. use coordinate notation to describe the transformation. explain your reasoning.

Explanation:

Step1: Identify the coordinates of corresponding points

Let's assume a point \(A\) on the red figure has coordinates \((x,y)\). For example, if we take a vertex of the red triangle. Suppose a vertex of the red triangle is \((1,1)\) and the corresponding vertex of the blue triangle is \((2,3)\).

Step2: Calculate the change in \(x\) and \(y\) - coordinates

The change in \(x\) - coordinate: \(2 - 1=1\). The change in \(y\) - coordinate: \(3 - 1 = 2\). In general, if a point \((x,y)\) on the red figure is transformed to a point \((x',y')\) on the blue figure, we can find the pattern. Let's check another pair of points. If another red - figure point is \((3,1)\) and the corresponding blue - figure point is \((4,3)\), again \(x'=x + 1\) and \(y'=y+2\).

Answer:

\((x,y)\to(x + 1,y + 2)\)