Question

in the standard (x, y) coordinate plane, what is the length of the line segment with endpoints at (1, 5) and (6, 2)? select one answer a $sqrt{34}$ b $sqrt{2}$ c $7sqrt{2}$ d 4 e 34

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute given points

Let $(x_1,y_1)=(1,5)$ and $(x_2,y_2)=(6,2)$. Substitute values:
$d=\sqrt{(6-1)^2+(2-5)^2}$

Step3: Calculate differences

Compute the terms inside the square root:
$d=\sqrt{(5)^2+(-3)^2}$

Step4: Simplify squared terms

Calculate the squares:
$d=\sqrt{25+9}$

Step5: Sum and simplify root

Add and simplify the square root:
$d=\sqrt{34}$

Answer:

A. $\sqrt{34}$