Question

The four vertices of a mobile are: \(A(5, −10), B(8, −10), C(8, −6)\) and \(D(5, −6).\) If we try to see them through a magnifying glass, the new vertices would be \(A'(7.5, −15), B'(12, −15), C'(12, −9),\) and \(D'(7.5, −9)\). What is the factor by which the image of the mobile is magnified?

Answer 1

\(A(5, −10) \rightarrow A'(7.5, −15)\)
The size by which the shape is enlarged or reduced is called its scale factor.
If the center of dilation is the origin, then the coordinates are multiplied by the scale factor: \((x, y) \Rightarrow (kx, ky),\) where k is the scale factor.
Let’s assume that the factor by which the image of the mobile is magnified is x.
So, \(A'(5 \times x, −10 \times x)\) corresponds to \(A'(7.5, −15).\)
This means, \(5 \times x = 7.5\).
\(\Rightarrow x = \dfrac{7.5}{5}\)
\(\Rightarrow x = 1.5\)
The image of the mobile is magnified by the factor of \(1.5\).
Similarly, we will do it for vertices \(B, C,\) and \(D\).

Hence, the correct answer is option A.