Question

the coordinates of a line segment are (1,6) and (11, -4). what is the length of the line segment? round your answer to the nearest tenth. a. 7.1 b. 14.1 c. 50 d. 200

Answer 1

The length of the line segment AB where $A(x_A;\ y_A)$ and $B(x_B;\ y_B)$

$|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

We have: $A(1;\ 6);\ B(11;-4)$

subtitute

$|AB|=\sqrt{(1-11)^2+(6-(-4))^2}=\sqrt{(-10)^2+10^2}=\sqrt{100+100}\\\\=\sqrt{100\cdot2}=\sqrt{100}\cdot\sqrt2=10\sqrt2\approx14.1$

Answer: b. 14.1