Question

show what you know
what are the new coordinates if the triangle with vertices (2,3), (4,1),
and (3,2) is reflected over the x - axis and then translated 2 units up?
(2, - 3), (4, - 1), (3, - 2)
(2, - 1), (4,0), (3, - 2)
(2,3), (4,1), (3,2)
(2, - 1), (4,1), (3,0)

Explanation:

Step1: Reflect over the x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\).
For the point \((2,3)\), after reflection over the \(x\) - axis, it becomes \((2,-3)\).
For the point \((4,1)\), after reflection over the \(x\) - axis, it becomes \((4,-1)\).
For the point \((3,2)\), after reflection over the \(x\) - axis, it becomes \((3,-2)\).

Step2: Translate 2 units up

When a point \((x,y)\) is translated \(k\) units up, the transformation rule is \((x,y)\to(x,y + k)\) (here \(k = 2\)).
For the point \((2,-3)\), after translation 2 units up: \((2,-3+2)=(2,-1)\).
For the point \((4,-1)\), after translation 2 units up: \((4,-1 + 2)=(4,1)\).
For the point \((3,-2)\), after translation 2 units up: \((3,-2+2)=(3,0)\).

Answer:

\([(2,-1),(4,1),(3,0)]\)