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irga5000 [103]
3 years ago
10

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 di

lation so that G' is located at (5, -5). Which algebraic representation represents this dilation?
Mathematics
1 answer:
Marizza181 [45]3 years ago
5 0

Answer:

The dilation on any point of the rectangle is P'(x,y) = \frac{5}{2}\cdot P(x,y).

Step-by-step explanation:

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

G'(x,y) = O(x,y) +k\cdot [G(x,y)-O(x,y)] (1)

Where:

G(x,y) - Coordinates of the point G, dimensionless.

O(x,y) - Center of dilation, dimensionless.

k - Scale factor, dimensionless.

G'(x,y) - Coordinates of the point G', dimensionless.

If we know that O(x,y) = (0,0), G(x,y) =(2,-2) and G'(x,y) =(5,-5), then scale factor is:

(5,-5) = (0,0) +k\cdot [(2,-2)-(0,0)]

(5,-5) = (2\cdot k, -2\cdot k)

k = \frac{5}{2}

The dilation on any point of the rectangle is:

P'(x,y) = (0,0) + \frac{5}{2}\cdot [P(x,y)-(0,0)]

P'(x,y) = \frac{5}{2}\cdot P(x,y) (2)

The dilation on any point of the rectangle is P'(x,y) = \frac{5}{2}\cdot P(x,y).

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