Question

2. 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. B 2 E E 2 4 16 A -2 -6 My 13

Answer 1

to find an equation of the line we need only 2 points, in this case E and C. First we need to calculate the slope

$m=\frac{2-0}{7-1}=\frac{2}{6}=\frac{1}{3}$

having the slope, we have that

$\begin{gathered} y-0=\frac{1}{3}(x-1)=\frac{1}{3}x-\frac{1}{3} \\ y=\frac{1}{3}x-\frac{1}{3} \end{gathered}$

so the equation for the line that pass through A E and C is

$y=\frac{1}{3}x-\frac{1}{3}$