Question

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what transformation is represented by the rule $(x,y)\to(x - 9,y + 2)$?
translation 9 units to the left and 2 units up
translation 9 units to the right and 2 units down
translation 9 units to the right and 2 units up
translation 9 units to the left and 2 units down

Explanation:

Step1: Analyze the x - coordinate change

For the x - coordinate, the rule is \(x\to x - 9\). When we subtract a positive number from \(x\) (in a coordinate \((x,y)\)), the point moves to the left. If \(x_1=x-9\), and \(9>0\), the horizontal movement is 9 units to the left.

Step2: Analyze the y - coordinate change

For the y - coordinate, the rule is \(y\to y + 2\). When we add a positive number to \(y\) (in a coordinate \((x,y)\)), the point moves up. If \(y_1=y + 2\), and \(2>0\), the vertical movement is 2 units up.

Answer:

translation 9 units to the left and 2 units up