Question

find the distance between a and b.
a. 9 units
b. \\( \sqrt { 82 } \\) units
c. \\( 4 \sqrt { 5 } \\) units
d. \\( \sqrt { 10 } \\) units

Explanation:

Step1: Find coordinates of A and B

From the graph, \(A(-4,-1)\) and \(B(5,0)\).

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

Here \(x_1=-4,y_1 = - 1,x_2=5,y_2=0\).
Substitute into formula: \(d=\sqrt{(5-(-4))^2+(0 - (-1))^2}\)

Step3: Simplify the expression

First, \(5-(-4)=5 + 4=9\) and \(0-(-1)=0 + 1=1\).
Then \(d=\sqrt{9^2+1^2}=\sqrt{81 + 1}=\sqrt{82}\)

Answer:

B. \(\sqrt{82}\) units