Question

recall that kai reflects a triangle across the x - axis, then translates it 3 units up. a different vertex of the triangle starts at the point (-1,2). what are the final coordinates of that vertex after both transformations? ( , )

Explanation:

Step1: Reflect across the x - axis

When reflecting a point \((x,y)\) across the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For the point \((-1,2)\), after reflection across the \(x\) - axis, it becomes \((-1,-2)\).

Step2: Translate 3 units up

When translating a point \((x,y)\) \(k\) units up, the rule is \((x,y)\to(x,y + k)\).
Here \(k = 3\), and the point after reflection is \((-1,-2)\). So, \((-1,-2)\to(-1,-2 + 3)\).

Answer:

\((-1,1)\)