Question

The triangle shown in the diagram is going to be dilated by a scale factor of 1/3. What is the length of the new side that corresponds to side AB?

A) 1
B) 3
C) 9
D) 1/3

Answer 1

It is A since AB is 3 units, dilated to a factor of 1/3  is 3/3 or 1

Answer 2

A. 1

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.

`D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2`, where,

`x_2-x_1`= Difference between two x-coordinates.

`y_2-y_1`= Difference between two y-coordinates of same x-coordinates.

Upon substituting our given values in distance formula we will get,

`\text{Length of side AB}=√((4-1)^2+(1-1)^2)`

`\text{Length of side AB}=√(3^2+0^2)`

`\text{Length of side AB}=√(9+0)`

`\text{Length of side AB}=√(9)=3`

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.

`\text{Length of the new side corresponding to side AB}=(1)/(3)* \text{Length of side AB}`

`\text{Length of the new side corresponding to side AB}=(1)/(3)* 3`

`\text{Length of the new side corresponding to side AB}=1`

Therefore, length of new side that corresponds to side AB is 1 unit and option A is the correct choice.