Question

a 3 - d printed model of a building has a corner at (2, 3, 4). the model is dilated from the origin by a scale factor of 2.5. what will be the new coordinates of that corner? (4.5, 5.5, 6.5) (5, 7.5, 10) (2, 3, 4) (8, 12, 16)

Explanation:

Step1: Multiply each coordinate by scale factor

When dilating a point \((x,y,z)\) from the origin by a scale factor \(k\), the new coordinates are \((kx,ky,kz)\). Here \(x = 2\), \(y=3\), \(z = 4\) and \(k=2.5\).
For \(x\)-coordinate: \(2\times2.5\)
For \(y\)-coordinate: \(3\times2.5\)
For \(z\)-coordinate: \(4\times2.5\)

Step2: Calculate each new coordinate

\(2\times2.5=5\)
\(3\times2.5 = 7.5\)
\(4\times2.5=10\)

Answer:

B. \((5,7.5,10)\)