Question

graph the image of square mnm after a dilation with a scale factor of \\( \frac { 1 } { 6 } \\) centered at the origin.

Explanation:

Step1: Find the coordinates of the original square

Assume the coordinates of the vertices of square \( KLMN \) (from the graph, if \( N=(2,10) \), \( M=(2, - 2) \), \( L=( - 2,-2) \), \( K=( - 2,10) \))

Step2: Apply the dilation formula

The formula for dilation centered at the origin \((x,y)\to(kx,ky)\) where \(k = \frac{1}{2}\).
For a point \((x,y)\) of the square, the new coordinates \((x',y')\) are given by \(x'=\frac{1}{2}x\) and \(y'=\frac{1}{2}y\).
If \(N=(2,10)\), then \(N'=(2\times\frac{1}{2},10\times\frac{1}{2})=(1,5)\)
If \(M=(2, - 2)\), then \(M'=(2\times\frac{1}{2},-2\times\frac{1}{2})=(1,-1)\)
If \(L=( - 2,-2)\), then \(L'=(-2\times\frac{1}{2},-2\times\frac{1}{2})=(-1,-1)\)
If \(K=( - 2,10)\), then \(K'=(-2\times\frac{1}{2},10\times\frac{1}{2})=(-1,5)\)

Step3: Plot the new points

Plot the points \(N'(1,5)\), \(M'(1,-1)\), \(L'(-1,-1)\), \(K'(-1,5)\) on the coordinate - plane and connect them to form the dilated square.

Answer:

Plot the points \((-1,5)\), \((1,5)\), \((1, - 1)\), \((-1,-1)\) and connect them to get the image of the square after dilation.