find the distance between the points a and b given below. (that is, find the length of the segment connecting a and b.) round your answer to the nearest hundredth.

Question

Accepted Answer

# Explanation:
## Step1: Determine the coordinates of points A and B
Assume the grid has standard coordinate system. Let’s say $A=(x_1,y_1)$ and $B=(x_2,y_2)$. From the grid (by counting units), if $A=(4,2)$ and $B=(7,6)$
## Step2: Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
Substitute $x_1 = 4,y_1 = 2,x_2=7,y_2 = 6$ into the formula:
$$
\begin{align*}
d&=\sqrt{(7 - 4)^2+(6 - 2)^2}\
&=\sqrt{3^2+4^2}\
&=\sqrt{9 + 16}\
&=\sqrt{25}\
&= 5
\end{align*}
$$
Another way (if coordinates are different due to grid interpretation error, assume horizontal distance $a$ and vertical distance $b$):
Suppose after counting units, the horizontal distance $a = 5$ units and vertical distance $b=4$ units (actual counting from grid).
$$
\begin{align*}
d&=\sqrt{a^{2}+b^{2}}\
&=\sqrt{5^{2}+4^{2}}\
&=\sqrt{25 + 16}\
&=\sqrt{41}\
&\approx6.40
\end{align*}
$$

# Answer:
$6.40$

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QUESTION IMAGE

Question

Explanation:

Step1: Determine the coordinates of points A and B

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Answer: