Segment \(AB\) measures 3 cm. Point \(O\) is the center of dilation. How long is the image of \(AB\) after a dilation with:

1. Scale factor 5?
2. Scale factor 3.7?
3. Scale factor \(\frac 1 5\)?
4. Scale factor \(s\)?

Here are points \(A\) and \(B\). Plot the points for each dilation described.

1. \(C\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of 2.
2. \(D\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of 2.
3. \(E\) is the image of \(B\) using \(A\) as the center of dilation and a scale factor of \(\frac 1 2\).
4. \(F\) is the image of \(A\) using \(B\) as the center of dilation and a scale factor of \(\frac 1 2\).

Make a perspective drawing. Include in your work the center of dilation, the shape you dilate, and the scale factor you use.

Triangle \(ABC\) and triangle \(DEF\) are scaled copies. Side \(AB\) measures 12 cm and is the longest side of \(ABC\). Side \(DE\) measures 8 cm and is the longest side of \(DEF\).

1. Triangle \(ABC\) is a scaled copy of triangle \(DEF\) with what scale factor?
2. Triangle \(DEF\) is a scaled copy of triangle \(ABC\) with what scale factor?

Here are 2 triangles.

Two triangles in an x y plane. Origin O. Horizontal axis from negative 6 to 6, by 1s. Vertical axis from negative 4 to 4, by 1s. Triangle A B C. Point A at negative 2 comma 4. Point B at negative 6 comma 1. Point C at negative 3 comma 1. Side A C is labeled 3 point 2. Side C B is labeled 3. Side A B is labeled 5. Triangle D E F. Point D at 3 comma negative 1. Point F at 4 comma negative 4. Point E at 7 comma negative 4. Angle F E D is labeled 36 point 9 degrees. Angle E D F is labeled 34 point 7 degrees. Angle D F E is labeled 108 point 4 degrees.

1. Show that the 2 triangles are congruent.
2. Find the side lengths of triangle \(DEF\) and the angle measures of triangle \(ABC\).