Question

5 q and c are points on a polygon. q and c are the points under a translation. find c. q(12,5) q(-2,7) c(-4,2) show your work here

Explanation:

Step1: Find translation vector

Let translation vector be \((h,k)\). For point \(Q(12,5)\) to \(Q'(-2,7)\), we have \(12 + h=-2\) and \(5 + k = 7\). Solving for \(h\): \(h=-2 - 12=-14\). Solving for \(k\): \(k = 7 - 5 = 2\). So translation vector is \((-14,2)\).

Step2: Apply translation to \(C\)

Point \(C(-4,2)\). To find \(C'\), add translation vector: \(x\)-coordinate: \(-4+(-14)=-18\), \(y\)-coordinate: \(2 + 2 = 4\). So \(C'(-18,4)\).

Answer:

\((-18, 4)\)