Question

directions: graph and label each figure and its im factor. assume all dilations use the origin as the cer 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: Recall the 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 is \((x',y')=(kx,ky)\).

Step2: Find the image of point \(A(-4,1)\)

For \(A(-4,1)\) with \(k = 3\), use the formula \((x',y')=(kx,ky)\).
\(x'=3\times(-4)=-12\), \(y'=3\times1 = 3\). So \(A'(-12,3)\).

Step3: Find the image of point \(B(-2,3)\)

For \(B(-2,3)\) with \(k = 3\), use the formula \((x',y')=(kx,ky)\).
\(x'=3\times(-2)=-6\), \(y'=3\times3 = 9\). So \(B'(-6,9)\).

Step4: Find the image of point \(C(0,-2)\)

For \(C(0,-2)\) with \(k = 3\), use the formula \((x',y')=(kx,ky)\).
\(x'=3\times0=0\), \(y'=3\times(-2)=-6\). So \(C'(0,-6)\).

Step5: Find the image of point \(D(-5,-2)\)

For \(D(-5,-2)\) with \(k = 3\), use the formula \((x',y')=(kx,ky)\).
\(x'=3\times(-5)=-15\), \(y'=3\times(-2)=-6\). So \(D'(-15,-6)\).

Answer:

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