find the length of line ab in the following diagram using the distance formula: b(-6,7) a(4,-4)

Question

Accepted Answer

# Explanation:
## Step1: Identify the coordinates
Let $A(x_1,y_1)=(4, - 4)$ and $B(x_2,y_2)=(-6,7)$
## Step2: Apply the distance formula
The distance formula is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
Substitute the values:
$$
\begin{align*}
d&=\sqrt{(-6 - 4)^2+(7-(-4))^2}\
&=\sqrt{(-10)^2+(7 + 4)^2}\
&=\sqrt{100+121}\
&=\sqrt{221}
\end{align*}
$$

# Answer:
$\sqrt{221}$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the coordinates

Step2: Apply the distance formula

Answer: