Question

directions: graph and label each figure and its imag

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

( b ( - 2,3 ) ), ( c ( 0, - 2 ) ), and ( d ( - 5, - 2 ) : k = 3 )
( a ^ { prime } ( )
( b ^ { prime } ( )
( c ^ { prime } ( )
( d ^ { prime } ( )

Explanation:

Step1: Recall the rule for dilation

When a point \((x,y)\) is dilated with a scale factor \(k\), the new point \((x',y')\) is given by \((x',y')=(kx,ky)\).

Step2: Find the coordinates of \(A'\)

For \(A(-4,1)\) and \(k = 3\), \(x'=3\times(-4)=-12\), \(y'=3\times1 = 3\). So \(A'(-12,3)\).

Step3: Find the coordinates of \(B'\)

For \(B(-2,3)\) and \(k = 3\), \(x'=3\times(-2)=-6\), \(y'=3\times3 = 9\). So \(B'(-6,9)\).

Step4: Find the coordinates of \(C'\)

For \(C(0,-2)\) and \(k = 3\), \(x'=3\times0=0\), \(y'=3\times(-2)=-6\). So \(C'(0,-6)\).

Step5: Find the coordinates of \(D'\)

For \(D(-5,-2)\) and \(k = 3\), \(x'=3\times(-5)=-15\), \(y'=3\times(-2)=-6\). So \(D'(-15,-6)\).

Answer:

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