Question

translate (2, 1) to the left 1 unit. then reflect the result over the y - axis. what are the coordinates of the final point?

Explanation:

Step1: Translate the point

When translating a point \((x,y)\) to the left by \(1\) unit, we subtract \(1\) from the \(x\) - coordinate.
For the point \((2,1)\), after translation to the left \(1\) unit, the new \(x\) - coordinate is \(2 - 1=1\), and the \(y\) - coordinate remains the same. So the translated point is \((1,1)\).

Step2: Reflect over the \(y\) - axis

When reflecting a point \((x,y)\) over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).
For the point \((1,1)\), after reflection over the \(y\) - axis, the \(x\) - coordinate becomes \(-1\) and the \(y\) - coordinate remains \(1\).

Answer:

\((-1,1)\)