Question

1. celia draws quadrilateral lmno on the coordinate grid. celia dilates quadrilateral lmno by a scale factor of 2 with a center of dilation at the origin to create figure lmno to represent the new outdoor eating area. which coordinate grid shows lmno?

Explanation:

Step1: Recall the rule of dilation

When a figure is dilated by a scale factor \(k\) with the center of dilation at the origin \((0,0)\), the coordinates of each point \((x,y)\) of the original figure change to \((kx,ky)\). Here \(k = 2\).

Step2: Analyze the original coordinates

Assume the original coordinates of the vertices of quadrilateral \(LMNO\) (from the given non - dilated figure). Let's say \(L(0,5)\), \(M(4,5)\), \(N(6,0)\), \(O(0,0)\).

Step3: Calculate the new coordinates after dilation

For point \(L(0,5)\): after dilation \(L'(0\times2,5\times2)=(0,10)\)
For point \(M(4,5)\): after dilation \(M'(4\times 2,5\times2)=(8,10)\)
For point \(N(6,0)\): after dilation \(N'(6\times2,0\times2)=(12,0)\)
For point \(O(0,0)\): after dilation \(O'(0\times2,0\times2)=(0,0)\)

Answer:

D.