Question

5* what is the length of the segment \\( \overline { a b } \\), given point a is located at \\( a ( 2,6 ) \\) and point b is located at \\( ( - 3,6 ) \\)? a. 5 units b. \\( 2 \sqrt { 10 } \\) units c \\( \sqrt { 5 } \\) units d. 10 units a b c d

Explanation:

Step1: Identify the formula for distance

For two points \((x_1,y_1)\) and \((x_2,y_2)\), the distance formula is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(A(2,6)\) so \(x_1 = 2,y_1=6\) and \(B(-3,6)\) so \(x_2=-3,y_2 = 6\).

Step2: Substitute values into the formula

Substitute \(x_1 = 2,y_1=6,x_2=-3,y_2 = 6\) into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Then \(d=\sqrt{(-3 - 2)^2+(6 - 6)^2}\).

Step3: Simplify the expression

First, calculate \((-3 - 2)^2=(-5)^2 = 25\) and \((6 - 6)^2=0^2=0\). So \(d=\sqrt{25+0}=\sqrt{25}\).

Step4: Calculate the square - root

Since \(\sqrt{25}=5\).

Answer:

A. 5 units