Question

A rancher maps, the coordinates for holding pen for his cows. How many fencing does the rancher need to enclose the cows holding pen?

Answer 1

The coordinates of the vertices of the rectangle are A'(x, y) = (3.5, 3.5), B'(x, y) = (3.5, 7), C'(x, y) = (10.5, 7) and D'(x, y) = (3.5, 10.5). The graph of the new pen is shown below.

We find a representation of a original pen, whose vertices are shown on Cartesian plane. The new pen is the result of dilating the original one by a scale factor of 3.5 and with center at the origin. The expression that describes the transformation is:

P'(x, y) = k · P(x, y)

Where:

P(x, y) - Original point

P'(x, y) - Resulting point

k - Scale factor

If we know that A(x, y) = (1, 1), B(x, y) = (1, 2), C(x, y) = (3, 2), D(x, y) = (1, 1) and k = 3.5, then the coordinates of the resulting point are:

A'(x, y) = 3.5 · (1, 1)

A'(x, y) = (3.5, 3.5)

B'(x, y) = 3.5 · (1, 2)

B'(x, y) = (3.5, 7)

C'(x, y) = 3.5 · (3, 2)

C'(x, y) = (10.5, 7)

D'(x, y) = 3.5 · (1, 3)

D'(x, y) = (3.5, 10.5)

The graph of the resulting rectangle is shown below.