Question

the figure below is dilated by a factor of 2 centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it.

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if a point \((x,y)\) is dilated, the new point \((x',y')\) is given by \((x',y')=(k x,k y)\). Here \(k = 2\).

Step2: Find new coordinates of point L

Let the coordinates of point \(L\) be \((- 3,-4)\). Then \(x=-3,y = - 4\), and \(x'=2\times(-3)=-6\), \(y'=2\times(-4)=-8\). So the new coordinates of \(L\) are \((-6,-8)\).

Step3: Find new coordinates of point P

Let the coordinates of point \(P\) be \((-2,2)\). Then \(x=-2,y = 2\), and \(x'=2\times(-2)=-4\), \(y'=2\times2 = 4\). So the new coordinates of \(P\) are \((-4,4)\).

Step4: Find new coordinates of point O

Let the coordinates of point \(O\) be \((3,3)\). Then \(x = 3,y=3\), and \(x'=2\times3=6\), \(y'=2\times3 = 6\). So the new coordinates of \(O\) are \((6,6)\).

Step5: Find new coordinates of point N

Let the coordinates of point \(N\) be \((3,-1)\). Then \(x = 3,y=-1\), and \(x'=2\times3=6\), \(y'=2\times(-1)=-2\). So the new coordinates of \(N\) are \((6,-2)\).

Step6: Find new coordinates of point M

Let the coordinates of point \(M\) be \((1,-1)\). Then \(x = 1,y=-1\), and \(x'=2\times1=2\), \(y'=2\times(-1)=-2\). So the new coordinates of \(M\) are \((2,-2)\).

Step7: Plot the new points

Plot the points \((-6,-8),(-4,4),(6,6),(6,-2),(2,-2)\) and connect them in the same order as the original figure to get the dilated image.

Answer:

Plot the points \((-6,-8),(-4,4),(6,6),(6,-2),(2,-2)\) and connect them to form the dilated figure.