Question

find the distance between a and b.
a. $2\sqrt{2}$ units
b. 3 units
c. $\sqrt{10}$ units
d. 2 units

Explanation:

Step1: Identify coordinates of A and B

Point A is at \((-1, 0)\), Point B is at \((2, 1)\).

Step2: Apply distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Substitute \(x_1 = -1\), \(y_1 = 0\), \(x_2 = 2\), \(y_2 = 1\):
\[

$$\begin{align*} d&=\sqrt{(2 - (-1))^2 + (1 - 0)^2}\\ &=\sqrt{(3)^2 + (1)^2}\\ &=\sqrt{9 + 1}\\ &=\sqrt{10} \end{align*}$$

\]

Answer:

C. \(\sqrt{10}\) units