Question

geometry ba 25 - 26
1 - 3: lesson quiz
what is the length of ab? round your answer to the nearest hundredth.

Explanation:

Step1: Identify coordinates

Let's assume point A has coordinates $(x_1,y_1)$ and point B has coordinates $(x_2,y_2)$. From the graph, if we assume A is at $(-5,-4)$ and B is at $(-3,3)$.

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 $x_1=-5,y_1 = - 4,x_2=-3,y_2 = 3$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(-3-(-5))^2+(3 - (-4))^2}\\ &=\sqrt{(-3 + 5)^2+(3 + 4)^2}\\ &=\sqrt{(2)^2+(7)^2}\\ &=\sqrt{4 + 49}\\ &=\sqrt{53} \end{align*}$$

\]

Step3: Calculate and round

$\sqrt{53}\approx7.28$

Answer:

$7.28$