In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7,2) and (1,0), respectively. Write an equation of the line that passes through points A, E, and C. -C
we know that
In a square, the diagonals are congruent
In the square ABCD, the line that passes through the point E and C, is the same line that contain the diagonal AC, because the diagonal passes through the midpoint E
so
Step 1
Find the equation of the line that passes through the points C(7,2) and E(1,0)
Find the slope
m=(0-2)/(1-7)
m=-2/-6
m=1/3
Find the equation of the line in slope intercept form
y=mx+b
we have
m=1/3
point (1,0)
substitute
0=(1/3)(1)+b
solve for b
0=(1/3)+b
b=-1/3
therefore
the equation of the line is
y=(1/3)x-1/3