Question

1. triangle abc with vertices a(-2,1), b(-2,-1), and c(2,-2) is transformed following rule (x,y)→(2x,2y). what are the coordinates of its image, triangle abc?

a. a(-2,2), b(-2,-2), and c(2,-4)
b. a(2,-2), b(2,2), and c(-2,4)
c. a(-4,1), b(-4,-1), c(4,-2)
d. a(-4,2), b(-4,-2), and c(4,-4)

Explanation:

Step1: Find the coordinates of \(A'\)

Given \(A(-2,1)\) and the rule \((x,y)\to(2x,2y)\).
For \(x = - 2\) and \(y = 1\), we have \(2x=2\times(-2)=-4\) and \(2y = 2\times1=2\). So \(A'(-4,2)\).

Step2: Find the coordinates of \(B'\)

Given \(B(-2,-1)\) and the rule \((x,y)\to(2x,2y)\).
For \(x=-2\) and \(y = - 1\), we have \(2x=2\times(-2)=-4\) and \(2y=2\times(-1)=-2\). So \(B'(-4,-2)\).

Step3: Find the coordinates of \(C'\)

Given \(C(2,-2)\) and the rule \((x,y)\to(2x,2y)\).
For \(x = 2\) and \(y=-2\), we have \(2x=2\times2 = 4\) and \(2y=2\times(-2)=-4\). So \(C'(4,-4)\).

Answer:

D. \(A'(-4,2)\), \(B'(-4,-2)\), and \(C'(4,-4)\)