I have a Problem with analytic of point A(1/2,-3) and B(a,2a) are given if $AB^2$=3/4 find the sum of possible values of a
How can we square B ? Is $AB^2$ a line or something?


closed as unclear what you're asking by José Carlos Santos, TheSimpliFire, Arnaud Mortier, Arnaud D., Ethan Bolker Feb 12 '18 at 12:59

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you have $$\vec{AB}=\left[a-\frac{1}{2};2a+3\right]$$ so we get $$(\vec{AB})^2=\left(a-\frac{1}{2}\right)^2+(2a+3)^2=\frac{3}{4}$$ this is the dot product and must be solved for $a$ $$\vec{AB}=[x_B-x_A;y_B-y_A]$$

  • $\begingroup$ I am new to analytic geometry can you explain how you get AB? $\endgroup$ – user530019 Feb 12 '18 at 8:55
  • $\begingroup$ can you proceed now? $\endgroup$ – Dr. Sonnhard Graubner Feb 12 '18 at 8:57
  • $\begingroup$ Can you please write the formula of dot product too? $\endgroup$ – user530019 Feb 12 '18 at 9:36
  • $\begingroup$ see here en.wikipedia.org/wiki/Dot_product $\endgroup$ – Dr. Sonnhard Graubner Feb 12 '18 at 10:43