Question

triangle pqr has coordinates p(-8,3), q(-8,6), and r(-3,6). if the triangle is translated by using the rule (x,y)→(x + 4,y - 6), what are the coordinates of triangle pqr? p(-4,-3), q(-4,0), r(1,0) p(-4,9), q(-4,12), r(1,12) p(-12,9), q(-12,12), r(-7,12) p(-4,7), q(-14,0), r(1,10)

Explanation:

Step1: Calculate the x - coordinate of \(P'\)

Given the translation rule \((x,y)\to(x + 4,y-6)\) and \(P(-8,3)\).
For the x - coordinate: \(x=-8\), using the formula \(x'=x + 4\), we have \(x'=-8 + 4=-4\).

Step2: Calculate the y - coordinate of \(P'\)

For the y - coordinate: \(y = 3\), using the formula \(y'=y-6\), we have \(y'=3-6=-3\). So \(P'(-4,-3)\).

Step3: Calculate the x - coordinate of \(Q'\)

Given \(Q(-8,6)\). For the x - coordinate: \(x=-8\), using \(x'=x + 4\), we have \(x'=-8 + 4=-4\).

Step4: Calculate the y - coordinate of \(Q'\)

For the y - coordinate: \(y = 6\), using \(y'=y-6\), we have \(y'=6-6 = 0\). So \(Q'(-4,0)\).

Step5: Calculate the x - coordinate of \(R'\)

Given \(R(-3,6)\). For the x - coordinate: \(x=-3\), using \(x'=x + 4\), we have \(x'=-3+4 = 1\).

Step6: Calculate the y - coordinate of \(R'\)

For the y - coordinate: \(y = 6\), using \(y'=y-6\), we have \(y'=6-6=0\). So \(R'(1,0)\).

Answer:

\(P'(-4,-3)\), \(Q'(-4,0)\), \(R'(1,0)\) (the first option)