Use the following information to answer the Questions
Seven board members of a company must decide between two other board members (A and B) for a certain position. The voters are concerned with two issues and their ideal points are represented as ordered pairs: (1, 4), (2, 3), (5, 2), (6, 3), (6, 1), (4, 4), and (3, 3). Assume that A and B announce policy positions of (1, 1) and (6, 4), respectively.
-What is the equation of the line which divides the two-dimensional space separating voters preferring A over B from those preferring B over A?

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Quizplus · Accepted Answer

The equation of the line that divides the two-dimensional space, separating voters preferring A over B from those preferring B over A, can be found by calculating the perpendicular bisector of the line segment joining the points representing A and B's policy positions, which are (1, 1) and (6, 4), respectively. The midpoint of this line segment is $\left(\frac{1+6}{2}, \frac{1+4}{2}\right) = \left(\frac{7}{2}, \frac{5}{2}\right)$, and the slope of the line segment is $\frac{4-1}{6-1} = \frac{3}{5}$. The slope of the perpendicular bisector is the negative reciprocal of $\frac{3}{5}$, which is $-\frac{5}{3}$. Using the point-slope form of a line, $y - y_1 = m(x - x_1)$, and substituting the midpoint and the slope of the perpendicular bisector, we can derive the equation of the line that separates voters for A and B. Simplifying this equation will give us $5x + 3y = 25$, which corresponds to choice A.

Use the Following Information to Answer the Questions Seven Board 5x+3y=255 x + 3 y = 255x+3y=25

Use the Following Information to Answer the Questions
Seven Board $5 x + 3 y = 25$