Question

dilation of a point
score: 0/3 penalty: none
question
what is the image of (9, -7) after a dilation by a scale factor of 4 centered at the origin?
answer attempt 1 out of 2

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if the original point is \((x,y)\), the image point \((x',y')\) is given by \((x',y')=(k\cdot x,k\cdot y)\).
Here \(k = 4\), \(x = 9\), and \(y=-7\).

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

Multiply the \(x\) - coordinate of the original point by the scale factor. \(x'=4\times9 = 36\).

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

Multiply the \(y\) - coordinate of the original point by the scale factor. \(y'=4\times(-7)=-28\).

Answer:

\((36,-28)\)