Question

(05.06A LC)

Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B'. What is the length

of A'B'?

1 unit

4 units

5 units

6 units

Answer 1

4 units

Explanation:

A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.

If a shape is transformed, the length of its sides and shape remains the same, only the position changes.

If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:

Let A be at (
`x_1,y_1`) and B be at (
`x_2,y_2`). The length of AB is:

`AB=√((y_2-y_1)^2+(x_2-x_1)^2)`

If AB is translated to the right by 1 unit the new points are A' at (
`x_1+1,y_1`) and B' at (
`x_2+1,y_2`). The length of A'B' is:

`A'B'=√((y_2-y_1)^2+(x_2+1-(x_1+1))^2)=√((y_2-y_1)^2+(x_2+1-x_1-1)^2)\\\\A'B'=√((y_2-y_1)^2+(x_2-x_1)^2)`

AB = A'B' = 4 units