Question

use the graph and the translation (x,y)→(x + 5,y - 4) to answer parts a and b below.
a. enter the image of each vertex as an ordered pair
r→r(x1 + 5,y1 - 4) (type an ordered pair.)
s→s(x2 + 5,y2 - 4) (type an ordered pair.)
t→t(x3 + 5,y3 - 4) (type an ordered pair.)
v→v(x4 + 5,y4 - 4) (type an ordered pair.)

Explanation:

Step1: Identify the translation rule

The translation rule is \((x,y)\to(x + 5,y-4)\). This means we add 5 to the \(x\) - coordinate and subtract 4 from the \(y\) - coordinate of each vertex.

Step2: Assume coordinates of vertices

Let the coordinates of vertex \(R\) be \((x_1,y_1)\), of vertex \(S\) be \((x_2,y_2)\), of vertex \(T\) be \((x_3,y_3)\) and of vertex \(V\) be \((x_4,y_4)\).

Step3: Find new coordinates for \(R\)

The new coordinates of \(R\), denoted as \(R'\) are \((x_1 + 5,y_1-4)\).

Step4: Find new coordinates for \(S\)

The new coordinates of \(S\), denoted as \(S'\) are \((x_2 + 5,y_2-4)\).

Step5: Find new coordinates for \(T\)

The new coordinates of \(T\), denoted as \(T'\) are \((x_3 + 5,y_3-4)\).

Step6: Find new coordinates for \(V\)

The new coordinates of \(V\), denoted as \(V'\) are \((x_4 + 5,y_4-4)\).

To get the actual ordered - pairs, you need to first determine the original coordinates \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\) and \((x_4,y_4)\) from the graph and then apply the above - mentioned calculations.

Answer:

If the original coordinates of \(R=(x_1,y_1)\), \(S=(x_2,y_2)\), \(T=(x_3,y_3)\), \(V=(x_4,y_4)\), then \(R'=(x_1 + 5,y_1-4)\), \(S'=(x_2 + 5,y_2-4)\), \(T'=(x_3 + 5,y_3-4)\), \(V'=(x_4 + 5,y_4-4)\)