Question

find the distance between the two points. (-8,10),(-6,7) \\( \sqrt { ( x _ { 2 } - x _ { 1 } ) ^ { 2 } + ( y _ { 2 } - y _ { 1 } ) ^ { 2 } } \\)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-8,10)\) and \((x_2,y_2)=(-6,7)\).

Step2: Substitute into the distance formula

Substitute \(x_1 = - 8\), \(y_1=10\), \(x_2=-6\), \(y_2 = 7\) into the formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

$$
LATEXBLOCK0
$$

Step3: Simplify the expressions inside the square - root

First, \(-6+8 = 2\) and \((-3)^2=9\), \((2)^2 = 4\). Then \(d=\sqrt{4 + 9}\).

Step4: Calculate the final result

Since \(4+9=13\), so \(d=\sqrt{13}\).

Answer:

\(\sqrt{13}\)