Question

directions: graph and label each figure and its image under the given dilation.

1. quadrilateral ( a b c d ) with vertices ( a(-4,1) ),

( b(-2,3), c(0,-2) ), and ( d(-5,-2): k = 3 )

1. triangle ( l m n ) with vertices ( l(2,-8), m(12,8) ),

and ( n(14,-4): k = 1 / 2 )

1. rectangle ( p q r s ) with vertices ( p(5,15) ),

( q(15,15), r(15,10) ), and ( s(5,10): k = 4 / 5 )

1. rhombus ( w x y z ) with vertices ( w(2,-4) ),

( x(6,-2), y(10,-4) ), and ( z(6,-6): k = 3 / 2 )

1. square ( m n o p ) with vertices ( m(-7,-4) ),

( n(-4,-3), o(-3,-6) ), and ( p(-6,-7): k = 2 )

1. trapezoid ( d e f g ) with vertices ( d(-5,15) ),

( e(10,10), f(10,5) ), and ( g(-5,0): k = 1 / 5 )

Explanation:

Step1: Dilation formula

For a point \((x,y)\) and a scale factor \(k\), the image after dilation is \((kx,ky)\).

Step2: Calculate \(A'\)

Given \(A(-4,1)\) and \(k = 3\), then \(A'=(-4\times3,1\times3)=(-12,3)\).

Step3: Calculate \(B'\)

Given \(B(-2,3)\) and \(k = 3\), then \(B'=(-2\times3,3\times3)=(-6,9)\).

Step4: Calculate \(C'\)

Given \(C(0,-2)\) and \(k = 3\), then \(C'=(0\times3,-2\times3)=(0,-6)\).

Step5: Calculate \(D'\)

Given \(D(-5,-2)\) and \(k = 3\), then \(D'=(-5\times3,-2\times3)=(-15,-6)\).

Answer:

\(A'(-12,3)\), \(B'(-6,9)\), \(C'(0,-6)\), \(D'(-15,-6)\)