Questions: Find the length of the line segment AB if the coordinates of the endpoints are A(-1,5) and B(3,11).

Find the length of the line segment AB if the coordinates of the endpoints are A(-1,5) and B(3,11).
Transcript text: $\qquad$ Find the length of the line segment $A B$ if the coordinates of the endpoints are $A(-1,5)$ and $B(3,11)$.
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Solution

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Solution Steps

Step 1: Find the difference in x-coordinates

The difference in the x-coordinates is 3 - (-1) = 4.

Step 2: Find the difference in y-coordinates

The difference in the y-coordinates is 11 - 5 = 6.

Step 3: Use the distance formula

The distance formula is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Plugging in the differences calculated above, the length of the line segment AB is $\sqrt{4^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52}$.

Step 4: Simplify the radical

$\sqrt{52}$ can be simplified to $2\sqrt{13}$.

Final Answer

The length of the line segment AB is $2\sqrt{13}$.

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