Question

triangle qrs has vertices q(8, -6), r(10, 5), and s(-3, 3). what are the coordinates of the vertices of the image of the triangle after a translation of ( t_{-7, 4}(x, y) )?
( q = )
( r = )
( s = )

Explanation:

Step1: Understand the translation rule

The translation \(T_{-7.6,4.3}(x,y)\) means we subtract \(7.6\) from the \(x -\) coordinate and add \(4.3\) to the \(y -\) coordinate of each vertex.
For vertex \(Q(8,-6)\):
\(x'=8 - 7.6\), \(y'=-6 + 4.3\)
\(x'=0.4\), \(y'=-1.7\)

Step2: Apply the rule to vertex \(R(10,5)\)

\(x'=10 - 7.6\), \(y'=5 + 4.3\)
\(x'=2.4\), \(y'=9.3\)

Step3: Apply the rule to vertex \(S(-3,3)\)

\(x'=-3 - 7.6\), \(y'=3 + 4.3\)
\(x'=-10.6\), \(y'=7.3\)

Answer:

\(Q'=(0.4,-1.7)\), \(R'=(2.4,9.3)\), \(S'=(-10.6,7.3)\)