Question

question 6 (multiple choice worth 1 points) (03.01rlc) ab has endpoints located at a(0, 0) and b(2, 0). it was dilated at a scale factor of \\( \frac { 1 } { 2 } \\) from center (2, 0). which statement describes the pre - image? ab is located at a(-1, 0) and b(1, 0) and is twice the length of ab. ab is located at a(-1, 0) and b(1, 0) and is half the length of ab. ab is located at a(-2, 0) and b(2, 0) and is twice the length of ab. ab is located at a(-2, 0) and b(2, 0) and is half the length of ab.

Explanation:

Step1: Calculate the length of \(A'B'\)

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). For \(A'(0,0)\) and \(B'(2,0)\), \(d=\sqrt{(2 - 0)^2+(0 - 0)^2}=2\).

Step2: Check each option

• Option1: For \(A(-1,0)\) and \(B(1,0)\), \(d=\sqrt{(1+1)^2+(0 - 0)^2}=2\). \(2

eq2\times2\).

• Option2: For \(A(-1,0)\) and \(B(1,0)\), \(d = 2\). \(2=\frac{1}{2}\times4\) (if \(A'B'\) was \(4\) which it's not).
• Option3: For \(A(-2,0)\) and \(B(2,0)\), \(d=\sqrt{(2 + 2)^2+(0 - 0)^2}=4\). \(4 = 2\times2\).
• Option4: For \(A(-2,0)\) and \(B(2,0)\), \(d = 4\). \(4

eq\frac{1}{2}\times2\).

Answer:

AB is located at A(-2,0) and B(2,0) and is twice the length of \(A'B'\)