Question

a triangle has vertices a(1,2),b(3,4),c(5,1). after a dilation with a scale factor of 2, what are the coordinates of b?
a. (0,0)
b. (6,8)
c. (3,6)
d. (1.5,2)

Explanation:

Step1: Recall dilation formula

For a dilation with scale - factor \(k\) about the origin, if a point \((x,y)\) is dilated, the new point \((x',y')\) has coordinates \((kx,ky)\). Here \(k = 2\) and the point \(B\) has coordinates \((3,4)\).

Step2: Calculate new coordinates

For point \(B(3,4)\), \(x'=k\times x\) and \(y'=k\times y\). Substitute \(k = 2\), \(x = 3\), and \(y = 4\) into the formulas. We get \(x'=2\times3 = 6\) and \(y'=2\times4 = 8\).

Answer:

B. \((6,8)\)