Question

a shape is translated according to the algebraic representation below. what is the pre - image of the point (2, 9)? (x, y) → (x - 3, y + 4) show your work here

Explanation:

Step1: Define pre - image variables

Let the pre - image of the point \((2,9)\) be \((x,y)\). According to the translation rule \((x,y)\to(x - 3,y + 4)\), we know that the image of \((x,y)\) is \((x-3,y + 4)=(2,9)\).

Step2: Solve for x - coordinate

We set up the equation for the x - coordinate: \(x-3 = 2\). To solve for \(x\), we add 3 to both sides of the equation. So \(x=2 + 3=5\).

Step3: Solve for y - coordinate

We set up the equation for the y - coordinate: \(y + 4=9\). To solve for \(y\), we subtract 4 from both sides of the equation. So \(y=9 - 4 = 5\).

Answer:

The pre - image of the point \((2,9)\) is \((5,5)\)