Question

What is the length of the segment whose endpoints are A(-4, 3) and B (10, 6)?

Answer 1

Apply Pythagoras:

length = sqrt( (10--4)² + (6-3)² ) = sqrt(205)

Answer 2

Answer:  The correct option is (B) $\sqrt{205}.$

Step-by-step explanation:  We are given to find the length of the segment whose endpoints are A(-4, 3) and B (10, 6).

We know that

the length of a line segment with endpoints (a, b) and (c, d) is calculated using distance formula as follows :

$D=\sqrt{(c-a)^2+(d-b)^2}.$

Therefore, using distance formula, the distance between the endpoints A(-4, 3) and B (10, 6) is given by

$AB\\\\=\sqrt{(10-(-4))^2+(6-3)^2}\\\\=\sqrt{(10+4)^2+3^2}\\\\=\sqrt{14^2+9}\\\\=\sqrt{196+9}\\\\=\sqrt{205}.$

Thus, the length of the line segment AB is $\sqrt{205}~\textup{units}.$

Option (B) is CORRECT.