Question

what is the length of the segment \\( \overline { a b } \\) shown in the graph?
a. 6 units
b. 8 units
c. 9 units
d. 10 units

Explanation:

Step1: Find coordinates of A and B

From the graph, \(A(-4,-3)\) and \(B(4,3)\).

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Here \(x_1=-4,y_1 = - 3,x_2=4,y_2 = 3\).
Substitute into formula: \(d=\sqrt{(4-(-4))^2+(3 - (-3))^2}=\sqrt{(4 + 4)^2+(3+3)^2}\)

Step3: Simplify the expression

\(d=\sqrt{8^2+6^2}=\sqrt{64 + 36}=\sqrt{100}\)

Step4: Calculate the square - root

\(\sqrt{100}=10\)

Answer:

d. 10 units