Question

geometry
dilations homework
name
state whether a dilation with the given scale factor is a reduction or an
enlargement

1. ( k = 4 ) 2. ( k=\frac{3}{4} ) 3. ( k=\frac{5}{2} ) 4. ( k = 0.26 )

determine whether the dilation is a reduction or an enlargement and find its scale
factor.

1. 6. 7.

use the origin as the center of the dilation and the given scale factor
to find the coordinates of the vertices of the image of the polygon.

1. ( k = 2 ) 9. ( k=\frac{1}{2} )

point ( a ) is a vertex of a polygon. point ( a^{prime} ) is the image of ( a ) after a dilation
centered at the origin. find the scale factor of the dilation.

1. ( a(-2,-3) ) and ( a^{prime}(-10,-15) ) 11. ( a(9,15) ) and ( a^{prime}(6,10) )

Explanation:

Step1: Recall the formula for scale factor

For a dilation centered at the origin, if \(A(x,y)\) and \(A'(x',y')\) are corresponding points, the scale factor \(k=\frac{x'}{x}=\frac{y'}{y}\) (assuming \(x
eq0,y
eq0\))

Step2: Solve for problem 10

Given \(A(-2,-3)\) and \(A'(-10,-15)\)
\(k=\frac{- 10}{-2}=\frac{-15}{-3}\)
\(k = 5\)

Step3: Solve for problem 11

Given \(A(9,15)\) and \(A'(6,10)\)
\(k=\frac{6}{9}=\frac{10}{15}\)
Simplify \(\frac{6}{9}=\frac{2}{3}\) and \(\frac{10}{15}=\frac{2}{3}\)

Answer:

1. \(k = 5\)
2. \(k=\frac{2}{3}\)