Question

The following figure shows a parallelogram $ABCD$ whose side $AB$ is parallel to $x-axis$, $\angle A={60}^o$ and vertex $C=(7,5)$. Find the equations of $BC$ and $CD$.

Answer 1

Given $C(7,5)$ and $\angle BAD={60}^{\circ }$

$AB\parallel x-axis$

consider th problem.

$\angle DAB=\angle CBE$

Hence, $\angle CBE={60}^{\circ }$ (corresponding angles of parallelogram $ABCD$)

Now, slope for the line $BC\left(m\right)=\tan {60}^{\circ }=\sqrt{3}$

Therefore, equation for the line $BC$ by point-slope formula.

$y-y_1=m(x=x_1)$

$y-5=\sqrt{3}(x-7)$

$y=\sqrt{3}x+5-7\sqrt{3}$

Now, for equation of line $CD$

Slope $\left(m_1\right)=\tan 0^{\circ }=0$, and passing through the points $(7,5)$

$y-y_1=m_1(x-x_1)$

$y-5=0(x-7)$

$y=5$

Hence the equation of sides $BC$ and $CD$ are $y=\sqrt{3}x+5-7\sqrt{3}$ and $y=5$ respectively.