Question

$STUV$ is a parallelogram with a perimeter of $14$. Find the y-coordinate of point T.

• A. $1.89$
• B. $1.26$
• C. $3.26$
• D. $3.89$
• E. $4.26$

Answer 1

Answer: (D)

In figure $S(3,2)$ and $V(7,2)$ and $\angle TSV={39}^o$

Then distance $SV=$ $\sqrt{(2-2{)}^2+(7-3{)}^2}=\sqrt{(4{)}^2}=4$

Then $ST=$ $\frac{14-2\times 4}{2}=3$

Draw perpendicular from point $T$ on line $SV$ that this cut at $X$

Then In right angled triangle $TXS$,

$\frac{ST}{TX}=\sin {39}^0$

$\Rightarrow \frac{TX}{3}=\sin {39}^0$

$\Rightarrow TX=3\times 0.6293$

$\Rightarrow TX=1.89$

The $y$ coordinates of point $S$ is $2$.

Then $y$-coordinates of point $T=2+1.89=3.89$