Question 46 Answer and Explanation _ACT April 2016 Form 73E Math Section

Use the following information to answer questions 46-48.

The points graphed in the standard (x, y) coordinate plane below show the positions of 5 stars in a plane relative to a point represented by the origin, where each coordinate unit equals 1 light-year. A light-year is the distance that light travels in 1 year, and 1 light-year≈5.9× ${10}^{12}$ miles. The distance from Star A to Star D is approximately 11.4 light-years. Star A has a mass of 3 solar masses; and Stars B, C, D, and E each have a mass of 1 solar mass.

46. Because Stars B, C, D, and E have the same mass, the position determined by the average of the x-coordinates and the average of the y-coordinates of those stars approximates the center of mass of those 4 stars. What are the coordinates of this position?

F. $\left({10,3\frac{1}{3}}\right)$

G. $\left({10,3\frac{2}{5}}\right)$

H. $\left({10,3\frac{3}{4}}\right)$

J. $\left({12,3\frac{1}{3}}\right)$

K. $\left({12,3\frac{3}{4}}\right)$

Answer and Explanation

Your Answer is

Correct Answer is K

Explanation