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

Answer:

Option A is correct.

AB = $\sqrt{2^2+6^2}$

Step-by-step 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;

$D= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

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

By distance formula:

Length of AB = $\sqrt{(4-(-2))^2+(3-1)^2}$

                     = $\sqrt{(4+2)^2+2^2} =\sqrt{6^2+2^2}$

Therefore, the length of line segment AB = $\sqrt{2^2+6^2}$