Question

△abc has coordinates of a(-6, -7), b(4, -2), and c(0, 7). find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.
a(-6, -7), b(4, -2), c(0, 7)
a(-12, -7), b(8, -2), c(0, 7)
a(-12, -14), b(8, -4), c(0, 14)
a(-3, -3.5), b(2, -1), c(0, 3.5)

Explanation:

Step1: Apply dilation formula

For a dilation centered at the origin with scale factor \(k\), the formula is \((x,y)\to(kx,ky)\). Here \(k = 2\).
For point \(A(-6,-7)\):
\(x=-6,y = -7\), after dilation \(x'=2\times(-6)=-12,y'=2\times(-7)=-14\)
For point \(B(4,-2)\):
\(x = 4,y=-2\), after dilation \(x'=2\times4 = 8,y'=2\times(-2)=-4\)
For point \(C(0,7)\):
\(x = 0,y = 7\), after dilation \(x'=2\times0=0,y'=2\times7 = 14\)

Answer:

A\((-12,-14)\), B\((8,-4)\), C\((0,14)\) (corresponding to the third option in the given choices)