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 formula for dilation

When a point \((x,y)\) is dilated with center at the origin and scale factor \(k\), the image of the point is \((kx,ky)\).

Step2: Apply the formula

Given point \(B(4,9)\) and scale factor \(k = 2\).
For the \(x\)-coordinate: \(x'=k\times x=2\times4 = 8\)
For the \(y\)-coordinate: \(y'=k\times y=2\times9=18\)

Answer:

\(B'(8,18)\)