Question

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. Which of the following is an equation of the line that passes through points $B$ and $D$?

• A. $y=-3x-1$
• B. $y=-3(x-1)$
• C. $y=-\frac{1}{3}x+4$
• D. $y=-\frac{1}{3}x-1$

Answer 1

The correct option is B $y=-3(x-1)$

$C=(7,2)$ and $E=(1,0)$

The slope of line $CE$ thus becomes $\frac{0-2}{1-7}=\frac{1}{3}$

Since diagonals of a square are perpendicular to each other, slope of line $BD$ would be $\frac{-1}{\frac{1}{3}}=-3$

We now have the slope of line $BD$, which is $-3$ and coordinates of a point which lies on $BD$, i.e. $E=(1,0)$

The equation thus becomes $y=-3x+(0+3)$

i.e. $y=-3(x-1)$