1.10 practice questions
1. determine the length of each line segment.
a) b)

Question

Accepted Answer

# Explanation:
## Step1: Identify the coordinates
For part a), the two points are $(2,1)$ and $(3,5)$.
For part b), the two points are $(-2,-1)$ and $(0,0)$.
## Step2: Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
For part a):
Let $(x_1,y_1)=(2,1)$ and $(x_2,y_2)=(3,5)$
$$
\begin{align*}
d&=\sqrt{(3 - 2)^2+(5 - 1)^2}\
&=\sqrt{1^2+4^2}\
&=\sqrt{1 + 16}\
&=\sqrt{17}
\end{align*}
$$
For part b):
Let $(x_1,y_1)=(-2,-1)$ and $(x_2,y_2)=(0,0)$
$$
\begin{align*}
d&=\sqrt{(0-(-2))^2+(0 - (-1))^2}\
&=\sqrt{2^2+1^2}\
&=\sqrt{4+1}\
&=\sqrt{5}
\end{align*}
$$

# Answer:
a) $\sqrt{17}$
b) $\sqrt{5}$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the coordinates

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

Answer: