Question

point p(6,4) is dilated with a scale factor of 1/2 about the origin. what are the coordinates of the image p after the dilation? (4,3) (2,1) (12,8) (3,2) clear my selection

Explanation:

Step1: Apply the dilation formula

When a point \((x,y)\) is dilated about the origin with a scale factor \(k\), the new coordinates \((x',y')\) are given by \(x' = kx\) and \(y'=ky\). Here \(x = 6\), \(y = 4\), and \(k=\frac{1}{2}\).

Step2: Calculate the \(x\) - coordinate of the image

\(x'=\frac{1}{2}\times6 = 3\)

Step3: Calculate the \(y\) - coordinate of the image

\(y'=\frac{1}{2}\times4=2\)

Answer:

\((3,2)\) (the fourth option)