Answer:
A. 1
Step-by-step explanation:
We are told that our given triangle is going to be dilated by a scale factor of 1/3. We are asked to find the length of the new side that corresponds to side AB.
First of all we will find the length of side AB using distance formula.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex], where,
[tex]x_2-x_1[/tex]= Difference between two x-coordinates.
[tex]y_2-y_1[/tex]= Difference between two y-coordinates of same x-coordinates.
Upon substituting our given values in distance formula we will get,
[tex]\text{Length of side AB}=\sqrt{(4-1)^2+(1-1)^2}[/tex]
[tex]\text{Length of side AB}=\sqrt{3^2+0^2}[/tex]
[tex]\text{Length of side AB}=\sqrt{9+0}[/tex]
[tex]\text{Length of side AB}=\sqrt{9}=3[/tex]
As new side of the given triangle will be dilated by a scale factor of 1/3, this means side of new triangle corresponding to side AB will be 1/3 of side AB.
[tex]\text{Length of the new side corresponding to side AB}=\frac{1}{3}\times \text{Length of side AB}[/tex]
[tex]\text{Length of the new side corresponding to side AB}=\frac{1}{3}\times 3[/tex]
[tex]\text{Length of the new side corresponding to side AB}=1[/tex]
Therefore, length of new side that corresponds to side AB is 1 unit and option A is the correct choice.
