Question

1. point b has coordinates (-2,-5). after a translation 4 units down, a reflection across the y - axis, and a translation 6 units up, what are the coordinates of the image?

Explanation:

Step1: Translation 4 units down

When a point \((x,y)\) is translated \(4\) units down, the \(y -\) coordinate changes. The rule is \((x,y)\to(x,y - 4)\).
For the point \(B(-2,-5)\), after translation \(4\) units down, we get \((-2,-5-4)=(-2,-9)\).

Step2: Reflection across the \(y -\) axis

When a point \((x,y)\) is reflected across the \(y -\) axis, the rule is \((x,y)\to(-x,y)\).
For the point \((-2,-9)\), after reflection across the \(y -\) axis, we get \((2,-9)\).

Step3: Translation 6 units up

When a point \((x,y)\) is translated \(6\) units up, the \(y -\) coordinate changes. The rule is \((x,y)\to(x,y + 6)\).
For the point \((2,-9)\), after translation \(6\) units up, we get \((2,-9 + 6)=(2,-3)\).

Answer:

\((2,-3)\)