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' is located at (5, -5). Which algebraic representation represents this dilation?

The dilation on any point of the rectangle is .

Step-by-step explanation:

From Linear Algebra, we define the dilation of a point by means of the following definition:

(1)

Where:

- Coordinates of the point G, dimensionless.

- Center of dilation, dimensionless.

- Scale factor, dimensionless.

- Coordinates of the point G', dimensionless.

If we know that , and , then scale factor is:

The dilation on any point of the rectangle is:

(2)

The dilation on any point of the rectangle is .

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.