Question

the triangle ( abc ) is a dilation of the triangle ( abc ). what is the scale factor of the dilation?
simplify your answer and write it as a proper fraction, an improper fraction, or a whole
number.

Explanation:

Step1: Find the length of a side in the original triangle

Let's consider side \(AC\). Point \(A(-2,-9)\) and point \(C(2,-5)\). Using the distance formula for vertical distance (since \(x -\)coordinates are different, but for dilation we can also use the grid - based approach). The length of \(AC\) is \(|-5-(-9)| = 4\) units.

Step2: Find the length of the corresponding side in the dilated triangle

Corresponding side \(A'C'\). Point \(A'(-1,-2)\) and point \(C'(-1, - 1)\). The length of \(A'C'\) is \(|-1-(-2)|=1\) unit.

Step3: Calculate the scale factor

The scale factor \(k\) of a dilation is given by \(k=\frac{\text{length of side in image}}{\text{length of side in pre - image}}\). So \(k = \frac{1}{4}\)

Answer:

\(\frac{1}{4}\)