Question

graph the image of square defg after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify the vertices of square DEFG

Let's assume the coordinates of the vertices are D(-5, -5), E(5, -5), F(5, 5), G(-5, 5) (by observing the grid - not exact without labels but for general process).

Step2: Apply the dilation formula

For a dilation centered at the origin with scale factor \(k = 2\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \((x',y')=(k\times x,k\times y)\).
For point D(-5, -5): \(x'=2\times(- 5)=-10\), \(y'=2\times(-5)=-10\), new D'(-10, -10).
For point E(5, -5): \(x'=2\times5 = 10\), \(y'=2\times(-5)=-10\), new E'(10, -10).
For point F(5, 5): \(x'=2\times5=10\), \(y'=2\times5 = 10\), new F'(10, 10).
For point G(-5, 5): \(x'=2\times(-5)=-10\), \(y'=2\times5 = 10\), new G'(-10, 10).

Step3: Graph the new square

Plot the points D'(-10, -10), E'(10, -10), F'(10, 10), G'(-10, 10) on the coordinate - plane and connect them to form the dilated square.

Answer:

Graph the square with vertices D'(-10, -10), E'(10, -10), F'(10, 10), G'(-10, 10) on the given coordinate - grid.