Question

find the distance between a and b

Explanation:

Step1: Identify coordinates of A and B

From the graph, point A has coordinates \((4, -3)\) and point B has coordinates \((1, 6)\).

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 \(x_1 = 4\), \(y_1 = -3\), \(x_2 = 1\), \(y_2 = 6\) into the formula:
\[

$$\begin{align*} d&=\sqrt{(1 - 4)^2 + (6 - (-3))^2}\\ &=\sqrt{(-3)^2 + (9)^2}\\ &=\sqrt{9 + 81}\\ &=\sqrt{90}\\ &= 3\sqrt{10} \end{align*}$$

\]

Answer:

The distance between A and B is \(3\sqrt{10}\) (or approximately \(9.4868\)).