Question

state the coordinate of the image of the given point b (4,9) under a dilation with center at the origin with the given scale factor of 2. b (-8,-18) b (2,4.5) b (9,4) b (8,18)

Explanation:

Step1: Recall the dilation formula

For a dilation with center at the origin \((0,0)\) and 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 \(k = 2\), \(x = 4\), and \(y = 9\).

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

Using the formula \(x'=kx\), substitute \(k = 2\) and \(x = 4\). So \(x'=2\times4=8\).

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

Using the formula \(y'=ky\), substitute \(k = 2\) and \(y = 9\). So \(y'=2\times9 = 18\).

Answer:

\(B'(8,18)\)