Question

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

Explanation:

Step1: Identify coordinates

Let \(A(-4, - 1)\) and \(B(5,0)\).

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

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

Step3: Simplify the expression

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

Answer:

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