Question

graph the polygon with the given vertices and its image after a dilation with scale factor ( k ).
( x(6,-1), y(-2,-4), z(1,2) ; k = 3 )

Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) and scale factor \(k\), the dilated point is \((kx,ky)\).
For \(X(6, - 1)\): \(X'(3\times6,3\times(-1))=(18,-3)\)
For \(Y(-2, - 4)\): \(Y'(3\times(-2),3\times(-4))=(-6,-12)\)
For \(Z(1,2)\): \(Z'(3\times1,3\times2)=(3,6)\)

Answer:

The original polygon has vertices \(X(6, - 1)\), \(Y(-2, - 4)\), \(Z(1,2)\) and the dilated polygon has vertices \(X'(18,-3)\), \(Y'(-6,-12)\), \(Z'(3,6)\). Plot these points on the coordinate - plane to get the required graphs.