Question

Two line segments, line AB and line CD, have endpoints at A(-5,11), B(3,5), C(9,3), and D(2,10). Which of the two lines segments is longer? Show evidence to support your claim.

Answer 1

We need to find the length of the line segments AB and CD

the formula to find the distance between two points ( x1 , y1 ) and ( x2 , y2 ) is :

$d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}$

The distance of the line segment AB:

A(-5,11) , B(3,5)

so,

$d_{AB}=\sqrt[]{(3--5)^2+(5-11)^2}=\sqrt[]{8^2+(-6)^2}=\sqrt[]{64+36}=\sqrt[]{100}=10$

The distance of the line segment CD:

C(9,3), D(2,10)

$d_{CD}=\sqrt[]{(2-9)^2+(10-3)^2}=\sqrt[]{(-7)^2+7^2}=\sqrt[]{49+49}=\sqrt[]{98}$

Compare the lengths:

$\begin{gathered} \sqrt[]{98}<\sqrt[]{100} \\ \sqrt[]{98}<10 \end{gathered}$

So, the line segment AB is greater then the line segment CD

So, the longer line segment is AB