Question

suppose you are given a triangle with the following coordinates, a(0, 0) , b(2, 3) and c(1, -2). apply the rule (x, y) → (x - 2 , y + 1). what will be the coordinates of the image? a:( , ) b:( , ) c:( , )

Explanation:

Step1: Apply transformation to A(0,0)

The transformation rule is \((x, y) \to (x - 2, y + 1)\). For point \(A(0,0)\), substitute \(x = 0\) and \(y = 0\) into the rule. So \(x - 2=0 - 2=-2\) and \(y + 1=0 + 1 = 1\). Thus, \(A'(-2,1)\).

Step2: Apply transformation to B(2,3)

For point \(B(2,3)\), substitute \(x = 2\) and \(y = 3\) into the rule \((x - 2, y + 1)\). We get \(x - 2=2 - 2 = 0\) and \(y + 1=3 + 1=4\). So \(B'(0,4)\).

Step3: Apply transformation to C(1,-2)

For point \(C(1,-2)\), substitute \(x = 1\) and \(y=-2\) into the rule \((x - 2, y + 1)\). We have \(x - 2=1 - 2=-1\) and \(y + 1=-2 + 1=-1\). So \(C'(-1,-1)\).

Answer:

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