Question

you do: check for understanding
m(-1,-2), k(-1,3), y(1,0)
to
m(-1.5,-3), k(-1.5,4.5), y(1.5,0)
part a: describe the transformation.
part b: algebraically represent the transformation.

Explanation:

Step1: Analyze the coordinates

Compare the \(x\) and \(y\) - coordinates of the original points \(M(-1,-2)\), \(K(-1,3)\), \(Y(1,0)\) and the transformed points \(M'(-1.5,-3)\), \(K'(-1.5,4.5)\), \(Y'(1.5,0)\).
For \(x\) - coordinates: \(\frac{- 1.5}{-1}=1.5\), \(\frac{-1.5}{-1}=1.5\), \(\frac{1.5}{1}=1.5\)
For \(y\) - coordinates: \(\frac{-3}{-2}=1.5\), \(\frac{4.5}{3}=1.5\), \(\frac{0}{0}\) (since \(0\times1.5 = 0\))

Step2: Determine the transformation type

Since each coordinate of the original points is multiplied by a non - zero constant (\(k = 1.5\)), the transformation is a dilation.

Step3: Represent the transformation algebraically

If the original point is \((x,y)\) and the transformed point is \((x',y')\), and the scale factor is \(k\). The algebraic rule for dilation is \((x,y)\to(kx,ky)\). Here \(k = 1.5=\frac{3}{2}\), so the rule is \((x,y)\to(\frac{3}{2}x,\frac{3}{2}y)\)

Answer:

Part A: The transformation is a dilation.
Part B: The algebraic representation of the transformation is \((x,y)\to(\frac{3}{2}x,\frac{3}{2}y)\)