Question

14 what is the length of segment (overline{ab}), given point a is located at (a(-8, 1)) and point b is located at (b(4, 6))?
a 13 units
b 169 units
c 17 units
d (2sqrt{13}) units

Explanation:

Step1: Recall distance formula

The distance formula 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: Identify coordinates

For point \(A(-8,1)\), \(x_1=-8\), \(y_1 = 1\); for point \(B(4,6)\), \(x_2 = 4\), \(y_2=6\).

Step3: Substitute into formula

Calculate \(x_2 - x_1=4-(-8)=12\), \(y_2 - y_1=6 - 1 = 5\). Then \(d=\sqrt{(12)^2+(5)^2}=\sqrt{144 + 25}=\sqrt{169}=13\).

Answer:

A. 13 units