Name: SAT Math Help & School Math Mastery
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In $△ A BC$ , $∠ A BC = 9 0^{\circ}$ , $B A = 6$ , and $BC = 8$ . Points $P_{1}, P_{2}, \dots, P_{1000}$ lie on hypotenuse $\overline{A C}$ so that $A P_{1} = P_{1} P_{2} = \dots = P_{999} P_{1000} = P_{1000} C$ . What is the length of the vector sum $B P_{1} + B P_{2} + \dots + B P_{1000}$ ?