Question

hexagon j k l m n p is dilated by a scale factor of 1.5 centered at the origin and then reflected over the x - axis to create hexagon jklmnp.
which coordinates are correct for the given vertices of hexagon jklmnp?
select the two correct coordinates.
n(-9,3)
l(5.5,-1.5)
m(-3,-9)
k(3,-6)
p(-5.5,-5.5)
j(-3.5,7.5)

Explanation:

Step1: Find original coordinates

From the graph, assume original coordinates: \(N(-6, -2)\), \(L(4, 1)\), \(M(2,-6)\), \(K(2,4)\), \(P(-4,5)\), \(J(-2,6)\)

Step2: Apply dilation formula \((x,y)\to(1.5x,1.5y)\)

For \(N(-6, -2)\): \((1.5\times(-6),1.5\times(-2))=(-9,-3)\)
For \(L(4,1)\): \((1.5\times4,1.5\times1)=(6,1.5)\)
For \(M(2,-6)\): \((1.5\times2,1.5\times(-6))=(3,-9)\)
For \(K(2,4)\): \((1.5\times2,1.5\times4)=(3,6)\)
For \(P(-4,5)\): \((1.5\times(-4),1.5\times5)=(-6,7.5)\)
For \(J(-2,6)\): \((1.5\times(-2),1.5\times6)=(-3,9)\)

Step3: Apply reflection over \(x -\)axis formula \((x,y)\to(x, - y)\)

For \(N(-9,-3)\): \(N'(-9,3)\)
For \(L(6,1.5)\): \(L'(6,-1.5)\)
For \(M(3,-9)\): \(M'(3,9)\)
For \(K(3,6)\): \(K'(3,-6)\)
For \(P(-6,7.5)\): \(P'(-6,-7.5)\)
For \(J(-3,9)\): \(J'(-3,-9)\)

Answer:

A. \(N'(-9,3)\)
D. \(K'(3,-6)\)