Question

dilate each of the figures in 1 - 4 by the given scale factor. image as well as an algebraic representation of the dilation. 1. scale factor: 1.5

Explanation:

1. First, identify the coordinates of the original points:

• Assume the coordinates of point \(A\) are \((- 3,-1)\), point \(B\) are \((-1,4)\), and point \(C\) are \((3,-1)\).

1. Then, use the dilation formula \((x',y')=(k x,k y)\) where \(k = 1.5\):

• For point \(A(-3,-1)\):
• \(x'_A=1.5\times(-3)=-4.5\)
• \(y'_A=1.5\times(-1)=-1.5\)
• So \(A'=(-4.5,-1.5)\)
• For point \(B(-1,4)\):
• \(x'_B=1.5\times(-1)=-1.5\)
• \(y'_B=1.5\times4 = 6\)
• So \(B'=(-1.5,6)\)
• For point \(C(3,-1)\):
• \(x'_C=1.5\times3 = 4.5\)
• \(y'_C=1.5\times(-1)=-1.5\)
• So \(C'=(4.5,-1.5)\)

Answer:

\(A'=(-4.5,-1.5)\), \(B'=(-1.5,6)\), \(C'=(4.5,-1.5)\)