In the xy-plane, the slope m of the line that passes through the points
(x1,y1) and
(x2,y2) is
m= Thus, the slope of the line through the points
C(7,2) and
E(1,0) is
,which simplifies to
=.Therefore, diagonal
AC has a slope of
.The other diagonal of the square is a segment of the line that passes through points
B and
D. The diagonals of a square are perpendicular, and so the product of the slopes of the diagonals is equal to
−1. Thus, the slope of the line that passes through
B and
D is
−3 because
(−3).Hence an equation of the line that passes through
B and
D can be written as
y=−3x+b, where
b is the y-intercept of the line. Since diagonal
BD will pass through the center of the square,
E(1,0),the equation
0=−3(1)+b holds. Solving this equation for b gives
b=3. Therefore, an equation of the line that passes through points B and D is
y=−3x+3,which can be rewritten as
y=−3(x−1)Choices A, C, and D are incorrect and may result from a conceptual error or a calculation error.