Question

directions: graph and label each figure and its ima

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 dilation rule

To dilate a point \((x,y)\) with a scale factor \(k\) centered at the origin, the new coordinates \((x',y')\) are given by \(x' = kx\) and \(y' = ky\).

Step2: Find \(A'\)

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

Step3: Find \(B'\)

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

Step4: Find \(C'\)

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

Step5: Find \(D'\)

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

Answer:

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