Question

translate $(-3,-1)$ to the right 1 unit. then reflect the result over the $y$-axis. what are the coordinates of the final point?

Explanation:

Step1: Translate the point to the right

When translating a point \((x,y)\) to the right by \(a\) units, the new \(x\)-coordinate is \(x + a\) and \(y\)-coordinate remains the same.
For the point \((-3,-1)\) translated \(1\) unit to the right:
\(x=-3 + 1=-2\), \(y=-1\). So the new point is \((-2,-1)\).

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 \((-2,-1)\) reflected over the \(y\)-axis:
\(x=-(-2) = 2\), \(y=-1\).

Answer:

\((2,-1)\)