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_{-7.6,4.3}(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 a point \((x,y)\), the new point after translation is \((x - 7.6,y + 4.3)\)

Step2: Find the coordinates of \(Q'\)

Given \(Q(8,-6)\), use the translation rule:
\(x=8\), \(y =-6\)
\(x'=8-7.6\), \(y'=-6 + 4.3\)
\(x'=0.4\), \(y'=-1.7\)
So \(Q'=(0.4,-1.7)\)

Step3: Find the coordinates of \(R'\)

Given \(R(10,5)\), use the translation rule:
\(x = 10\), \(y=5\)
\(x'=10-7.6\), \(y'=5 + 4.3\)
\(x'=2.4\), \(y'=9.3\)
So \(R'=(2.4,9.3)\)

Step4: Find the coordinates of \(S'\)

Given \(S(-3,3)\), use the translation rule:
\(x=-3\), \(y = 3\)
\(x'=-3-7.6\), \(y'=3 + 4.3\)
\(x'=-10.6\), \(y'=7.3\)
So \(S'=(-10.6,7.3)\)

Answer:

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