Question

in which quadrant will the image of ( a(4, - 2) ) lie after dilation ( d_{-2} )?

Explanation:

Step1: Apply dilation formula

For a dilation \(D_{k}\) with scale factor \(k\), if a point \(P(x,y)\) is dilated, the image \(P'(x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(k=- 2\), \(x = 4\), \(y=-2\). So \(x'=-2\times4=-8\) and \(y'=-2\times(-2) = 4\).

Step2: Determine the quadrant

The quadrants are divided as follows: Quadrant I \((+,+)\), Quadrant II \((-,+)\), Quadrant III \((-,-)\), Quadrant IV \((+,-)\). The image point is \((-8,4)\) which has a negative \(x\) - coordinate and a positive \(y\) - coordinate.

Answer:

The image of \(A(4, - 2)\) after dilation \(D_{-2}\) lies in Quadrant II.