A rectangle has vertices E(4,8), F(2,8), G(2,-2) and H(-4,-2). The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,5). Which algebraic reprensentation represents this dilation

Note: The image of G after the dilation must be G'(5,-5) instead of G'(5,5).

Given:

The vertices of a rectangle are E(4,8), F(2,8), G(2,-2) and H(-4,-2).

The rectangle is dilated with the origin as the center of dilation so that G's is located at (5,-5).

To find:

The algebraic representation that represents this dilation.

Solution:

If a figure is dilated by factor k with origin as the center of dilation, then the dilation is defined as:

             ...(i)

Let the given rectangle is dilated by factor k with origin as the center of dilation. Then,

The image of G after dilation is G'(5,-5). So,

On comparing both sides, we get

So, the scale factor is .

Substituting in (i), we get

Therefore, the required algebraic representation to represents this dilation is .