Question

Draw the image of triangle ABC under a dilation whose center is P and scale factor is 1/2

Answer 1

Let:

`\begin{gathered} P=(0,0) \\ A=(8,-8) \\ B=(12,-12) \\ C=(0,-10) \end{gathered}`

Since the scale factor is 1/2:

`\begin{gathered} D_(O,k)(x,y)=(k(x-a)+a,k(y-b)+b) \\ O=P=(a,b)=(0,0) \end{gathered}`

Therefore:

`\begin{gathered} A\to(k(x+0)+0,k(y-0)+0)\to A^(\prime)=(4,-4) \\ B\to(k(x+0)+0,k(y-0)+0)B^(\prime)=(6,-6) \\ C\to(k(x+0)+0,k(y-0)+0)\to C^(\prime)=(0,-5) \end{gathered}`