Question

lesson 08: visualizing and graphing data
lesson 08: visualizing and graphing data
score: 25.5/100 answered: 5/15
question 6
find the distance between the points $\left(-\frac{7}{2},2\
ight)$ and $\left(-\frac{5}{2},\frac{7}{2}\
ight)$. give the exact distance.
exact distance =
make sure to fully simplify any radicals in your answer.
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Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=-\frac{7}{2},y_1 = 2,x_2=-\frac{5}{2},y_2=\frac{7}{2}$.

Step2: Calculate $x_2 - x_1$

$x_2 - x_1=-\frac{5}{2}-(-\frac{7}{2})=-\frac{5}{2}+\frac{7}{2}=\frac{-5 + 7}{2}=1$.

Step3: Calculate $y_2 - y_1$

$y_2 - y_1=\frac{7}{2}-2=\frac{7}{2}-\frac{4}{2}=\frac{7 - 4}{2}=\frac{3}{2}$.

Step4: Substitute into distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{1^2+(\frac{3}{2})^2}=\sqrt{1+\frac{9}{4}}=\sqrt{\frac{4 + 9}{4}}=\sqrt{\frac{13}{4}}=\frac{\sqrt{13}}{2}$.

Answer:

$\frac{\sqrt{13}}{2}$