Question

Which expression can be used to determined the length of segment AB?

Answer 1

An extension of the Pythagorean Theorem is the so-called "distance formula":

d^2=(y2-y1)^2+(x2-x1)^2

d^2=(3-1)^2+(4--2)^2

d^2=2^2+6^2

d=√(2^2+6^2)

Answer 2

Option A is correct.

AB =
`√(2^2+6^2)`

Explanation:

From the figure, we have the coordinates:

A= (4, 3) and B = (-2, 1)

Using distance formula(D) for two points
`(x_1, y_1)` and
`(x_2, y_2)` is given by;

`D= √((x_1-x_2)^2+(y_1-y_2)^2)`

Using the points of A = (4, 3) and B = (-2, 1)

By distance formula:

Length of AB =
`√((4-(-2))^2+(3-1)^2)`

=
`√((4+2)^2+2^2) =√(6^2+2^2)`

Therefore, the length of line segment AB =
`√(2^2+6^2)`