Question

a triangle with vertices at a(2,3), b(4,3) and c(2,6) is dilated by a scale factor of 2 with the center of dilation at the origin. what are the coordinates of the image of c? (4,12) (0,12) (1,3) (2,12)

Explanation:

Step1: Recall the dilation formula

When a point \((x,y)\) is dilated by a scale factor \(k\) with the center of dilation at the origin \((0,0)\), the formula for the image of the point is \((kx,ky)\).

Step2: Apply the formula to point \(C(2,6)\)

Here, \(x = 2\), \(y=6\) and \(k = 2\).
For the \(x\)-coordinate of the image: \(k\times x=2\times2 = 4\).
For the \(y\)-coordinate of the image: \(k\times y=2\times6=12\).

Answer:

A. \((4,12)\)