Question

for the graph shown to the right, find (a) ab to the nearest tenth and (b) the coordinates of the mid - point of ab. (a) ab = (round to the nearest tenth as needed.)

Explanation:

Step1: Identify coordinates of A and B

Assume A$(x_1,y_1)$ and B$(x_2,y_2)$ from the graph. Let's say A$(- 2,-2)$ and B$(2,3)$.

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 $x_1=-2,y_1 = - 2,x_2 = 2,y_2=3$ into the formula:
\[

$$\begin{align*} AB&=\sqrt{(2-(-2))^2+(3 - (-2))^2}\\ &=\sqrt{(2 + 2)^2+(3 + 2)^2}\\ &=\sqrt{4^2+5^2}\\ &=\sqrt{16 + 25}\\ &=\sqrt{41}\approx6.4 \end{align*}$$

\]

Answer:

$6.4$