Question

question
what is the image of $(8,-2)$ after a dilation by a scale factor of $\frac{1}{2}$ centered at the origin?
answer

Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) dilated by a scale factor \(k\) centered at the origin, the new point is \((kx,ky)\). Here \(x = 8\), \(y=-2\), \(k=\frac{1}{2}\).

Step2: Calculate new \(x\)-coordinate

Multiply \(x\)-coordinate by \(k\): \(k\times x=\frac{1}{2}\times8 = 4\)

Step3: Calculate new \(y\)-coordinate

Multiply \(y\)-coordinate by \(k\): \(k\times y=\frac{1}{2}\times(-2)=-1\)

Answer:

\((4,-1)\)