Question

after dilating a point (3,5) by a factor of 3, what will its new coordinates be?

a. (12,20)

b. (6,10)

c. (3,5)

d. (9,15)

Explanation:

Step1: Recall dilation rule

To dilate a point \((x,y)\) by a scale factor \(k\), we multiply each coordinate by \(k\), so the new point is \((kx,ky)\).

Step2: Apply dilation to \((3,5)\)

Here, \(x = 3\), \(y = 5\), and \(k = 3\). Multiply \(x\)-coordinate: \(3\times3 = 9\). Multiply \(y\)-coordinate: \(5\times3 = 15\). So the new coordinates are \((9,15)\).

Answer:

d. \((9,15)\)