Question

triangle abc was dilated using the rule d_3/4. triangle abc is the result of the dilation. what is ob? 1.5 units 3 units 4.5 units 6 units

Explanation:

Step1: Recall the dilation formula

If a dilation is centered at the origin with scale factor \(k\), then for a point \(P(x,y)\) and its image \(P'(x',y')\), we have \(OP'=k\times OP\). Here, the scale factor \(k = 3\) (since the ratio of \(OA\) to \(OA'\) is \(\frac{1}{3}\), and \(OB'=k\times OB\)). Let \(OB = 1.5\) units.

Step2: Calculate \(OB'\)

Using the formula \(OB'=k\times OB\), substitute \(k = 3\) and \(OB=1.5\). So \(OB'=3\times1.5\).

$$OB' = 4.5$$

Answer:

4.5 units