Question

help me solve this view an example get more help find the coordinates of p under the transformation t (0,4) o y - axis. the coordinates of p are (type an ordered pair.)

Explanation:

1. First, assume the original coordinates of point \(P\) are \((x,y)\). From the graph (although the point - \(P\) is not clearly labeled with coordinates, we'll use the general rules of transformations).

• The transformation \(T=(0,4)\circ y - axis\) means two - step transformation. First, reflect the point across the \(y\) - axis, and then translate it 4 units up.
• Let the original coordinates of point \(P\) be \((x,y)\).
• Step 1: Reflection across the \(y\) - axis
• The rule for reflecting a point \((x,y)\) across the \(y\) - axis is \((x,y)\to(-x,y)\). After reflection across the \(y\) - axis, the coordinates of the point become \((-x,y)\).
• Step 2: Translation 4 units up
• The rule for translating a point \((a,b)\) 4 units up is \((a,b)\to(a,b + 4)\). Applying this to the point \((-x,y)\) (the result of the first - step), we get \((-x,y + 4)\).

1. If we assume the original coordinates of point \(P\) are \((2,-1)\) (by visually estimating from the grid, if the grid has a unit length of 1).

• After reflection across the \(y\) - axis:
• Using the rule \((x,y)\to(-x,y)\), for \(x = 2\) and \(y=-1\), the point becomes \((-2,-1)\).
• After translation 4 units up:
• Using the rule \((a,b)\to(a,b + 4)\), for \(a=-2\) and \(b=-1\), we have \((-2,-1 + 4)=(-2,3)\).

Answer:

\((-2,3)\)