Question

8 select the correct answer from each drop - down menu.
overline{ab} is dilated by a scale factor of 3 to form overline{ab}. point o, which lies on overline{ab}, is the center of dilation.
the slope of overline{ab} is 3. the slope of overline{ab} is
overline{ab} through point o.
1/3

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Explanation:

Step1: Properties of dilation

Dilation is a transformation that changes the size of a figure but not its shape. When a line segment is dilated with a center of dilation on the line segment itself, the slope of the original line segment and the dilated line segment remains the same.

Step2: Determine the slope

Since \(\overline{AB}\) is dilated to form \(\overline{A'B'}\) with a center of dilation \(O\) on \(\overline{AB}\), and the slope of \(\overline{AB}\) is \(3\), the slope of \(\overline{A'B'}\) is also \(3\).

Step3: Position of \(\overline{A'B'}\)

Because the center of dilation \(O\) lies on \(\overline{AB}\) and we are performing a dilation, \(\overline{A'B'}\) passes through point \(O\).

Answer:

The slope of \(\overline{A'B'}\) is \(3\). \(\overline{A'B'}\) passes through point \(O\).