Question

a rectangle has vertices a(1,2), b(5,2), c(5,4), and d(1,4). it is translated to a(0,0), b(4,0), c(4,2), and d(0,2). what is the translation rule? a. (x - 1,y + 2) b. (x + 1,y + 2) c. (x - 1,y - 2) d. (x - 2,y - 2)

Explanation:

Step1: Analyze x - coordinate change

For point A(1, 2) to A'(0, 0), the change in x - coordinate is \(0 - 1=- 1\). For point B(5, 2) to B'(4, 0), the change in x - coordinate is \(4 - 5=-1\). In general, the change in x - coordinate for any point \((x,y)\) is \(x'=x - 1\).

Step2: Analyze y - coordinate change

For point A(1, 2) to A'(0, 0), the change in y - coordinate is \(0 - 2=-2\). For point C(5, 4) to C'(4, 2), the change in y - coordinate is \(2 - 4=-2\). In general, the change in y - coordinate for any point \((x,y)\) is \(y'=y - 2\). So the translation rule is \((x,y)\to(x - 1,y - 2)\).

Answer:

c. \((x,y)\to(x - 1,y - 2)\)