Respuesta :

GoddessofDork

So the distance formula is [tex] \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex] . Using the points that we have, we can solve for it as such:

[tex] \sqrt{(3-(-\frac{3}{5}))^2+(-2-(-\frac{7}{3}))^2} [/tex]

  1. Firstly, solve the subtraction: [tex] \sqrt{(\frac{18}{5})^2+(\frac{1}{3})^2} [/tex]
  2. Next, solve the exponents: [tex] \sqrt{\frac{324}{25}+\frac{1}{9}} [/tex]
  3. Next, we need to find the LCM of 9 and 25. To find the LCM, or least common multiple, find the lowest common number that they both multiply to. In this case, it's 225. Multiply 3234/25 by 9/9 and 1/9 by 25/25: [tex] \frac{324}{25}*\frac{9}{9}=\frac{2916}{225}\\\\ \frac{1}{9}*\frac{25}{25}=\frac{25}{225}\\ \\ \sqrt{\frac{2916}{225}+\frac{25}{225}} [/tex]
  4. Next, add the two fractions together, and your exact distance is [tex] \sqrt{\frac{2941}{225}} [/tex] (or approximately 3.62, rounded to the hundreths, if you square root the fraction.)

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