Question

directions: graph and label each figure and its ima
factor. assume all dilations use the origin as the cen
image.

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}(quad,quad) )
( b^{prime}(quad,quad) )
( c^{prime}(quad,quad) )
( d^{prime}(quad,quad) )

Explanation:

Step1: Apply dilation formula

When a point \((x,y)\) is dilated with a scale factor \(k\) and center at the origin \((0,0)\), the formula for the image of the point is \((x',y')=(kx,ky)\)

Step2: Find coordinates of \(A'\)

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

Step3: Find coordinates of \(B'\)

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

Step4: Find coordinates of \(C'\)

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

Step5: Find coordinates of \(D'\)

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

Answer:

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