Question

quadrilateral rust has a vertex at r(1,5). what are the coordinates of r after the translation (x,y)→(x + 1,y - 2), followed by a dilation by a scale factor of 3 centered at the origin?

Explanation:

Step1: Apply Translation

The translation rule is \((x, y) \to (x + 1, y - 2)\). For point \(R(1, 5)\), substitute \(x = 1\) and \(y = 5\) into the translation formula.
\(x\)-coordinate after translation: \(1 + 1 = 2\)
\(y\)-coordinate after translation: \(5 - 2 = 3\)
So, the coordinates after translation are \((2, 3)\).

Step2: Apply Dilation

The dilation rule with scale factor \(k = 3\) centered at the origin is \((x, y) \to (kx, ky)\). For the point \((2, 3)\) (after translation), substitute \(x = 2\), \(y = 3\), and \(k = 3\) into the dilation formula.
\(x\)-coordinate after dilation: \(3\times2 = 6\)
\(y\)-coordinate after dilation: \(3\times3 = 9\)

Answer:

The coordinates of \(R'\) are \((6, 9)\)