Question

find the distance between the given pair of points. p1: (2/3, 3/8) p2: (4/3, 7/8) the distance between p1 and p2 is . (round to two decimal places.)

Explanation:

Step1: Identify 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 $x_1=\frac{2}{3},y_1 = \frac{3}{8},x_2=\frac{4}{3},y_2=\frac{7}{8}$.

Step2: Calculate $x_2 - x_1$ and $y_2 - y_1$

$x_2 - x_1=\frac{4}{3}-\frac{2}{3}=\frac{4 - 2}{3}=\frac{2}{3}$; $y_2 - y_1=\frac{7}{8}-\frac{3}{8}=\frac{7 - 3}{8}=\frac{4}{8}=\frac{1}{2}$.

Step3: Square the differences

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

Step4: Find the sum of the squares

$\frac{4}{9}+\frac{1}{4}=\frac{4\times4}{9\times4}+\frac{1\times9}{4\times9}=\frac{16}{36}+\frac{9}{36}=\frac{16 + 9}{36}=\frac{25}{36}$.

Step5: Calculate the square - root

$d=\sqrt{\frac{25}{36}}=\frac{5}{6}\approx0.83$.

Answer:

$0.83$