Question

For the dilation with a center (0,0) shown on the graph, your friend says the scale factor is 5/2. What is the correct scale factor? What mistake did your friend likely make?

Answer 1

Answer:

From the given figure:

Coordinates of Pre-image triangle ABC are:

A (0, 5), B(-5, 0) and C(5, -5)

and

Coordinate of image triangle A'B'C' are;

A'(0, 2), B'(-2, 0) and C'(2, -2)

The rule of dilation with scale factor k and centered at origin is given by;

$(x, y) \rightarrow (kx, ky)$

To find k;

$A(0, 5) \rightarrow A'(k(0), k(5))$

A'(0, 2) = A'(0, 5k)

Comparing both sides we get;

5k = 2

$k = \frac{2}{5}$

Therefore, correct scale factor is $\frac{2}{5}$

He did mistake in transformations i.e a huge mistake mathematically.