Question

describe the transformation
this transformation can be described by $(x,y)=(square,square)$

Explanation:

Step1: Analyze the horizontal (x - coordinate) change

Take a point from figure 1, say \((x_1,y_1)\). Let's assume a vertex of figure 1 is \((2,3)\) and the corresponding vertex of figure 2 is \((2,- 4)\). The \(x\) - coordinate remains the same. So, \(x'=x\).

Step2: Analyze the vertical (y - coordinate) change

For the same pair of vertices \((2,3)\) and \((2,-4)\), we use the formula \(y'=y + k\). Substituting \(y = 3\) and \(y'=-4\), we get \(-4=3 + k\). Solving for \(k\): \(k=-4 - 3=-7\). So, \(y'=y-7\).

Answer:

\((x',y')=(x,y - 7)\)