Question

name
lesson 6 exit ticket
kwpn, kwpn, and kwpn are shown on the coordinate grid.
complete the chart below.

Explanation:

Transformation 1

Written Description

• Step1: Analyze the x - coordinates

For point \(K(-5,4)\) and \(K'(5,4)\), \(x\) changes from \(-5\) to \(5\). For point \(W(-5,0)\) and \(W'(5,0)\), \(x\) changes from \(-5\) to \(5\). For point \(P(-7,0)\) and \(P'(7,0)\), \(x\) changes from \(-7\) to \(7\). For point \(N(-8,2)\) and \(N'(8,2)\), \(x\) changes from \(-8\) to \(8\). The \(y\) - coordinates remain the same.
The transformation is a reflection over the \(y\) - axis.

Algebraic Description

• Step2: Use the reflection formula

The formula for a reflection over the \(y\) - axis is \((x,y)\to(-x,y)\)

Transformation 2

Written Description

• Step1: Analyze the coordinate ratios

For point \(K(-5,4)\) and \(K''(20,16)\), \(\frac{20}{- 5}=-4\) and \(\frac{16}{4} = 4\). For point \(W(-5,0)\) and \(W''(20,0)\), \(\frac{20}{-5}=-4\) and \(\frac{0}{0}\) (we can also check other points). For point \(P(-7,0)\) and \(P''(28,0)\), \(\frac{28}{-7}=-4\). For point \(N(-8,2)\) and \(N''(32,8)\), \(\frac{32}{-8}=-4\) and \(\frac{8}{2}=4\).
The transformation is a dilation with a scale factor of \(4\) centered at the origin (since \((x,y)\to(-4x,4y)\) which is equivalent to a dilation \(r = 4\) from the origin when considering the absolute value of the scale - factor for each coordinate direction)

Algebraic Description

• Step2: Use the dilation formula

The formula for a dilation centered at the origin is \((x,y)\to(kx,ky)\), here \(k = 4\) and considering the sign change (which is part of the dilation transformation rules when the scale factor is negative in one or both axes), \((x,y)\to(-4x,4y)\)

Answer:

	Transformation 1	Transformation 2
Algebraic Description	\((x,y)\to(-x,y)\)	\((x,y)\to(-4x,4y)\)