In Figure STUV is a parallelogram with a perimeter of 14. What is the y - coordinate of point T ?

Options

A. `1.26`
B. `1.89`
C. `3.26`
D. `3.89`

Answer

D

Explanation

The perimeter of any polygon is the sum of the lengths of its sides. Since points S and V have the same y - coordinate of 2, SV is parallel to the x - axis. The length of SV is the positive difference of the x - coordinates of points V and S. The length of SV is `7-3=4`. Opposite sides of a parallelogram are equal, so the length of TU is also 4. ST and UV are opposite sides of parallelogram STUV, so ST and UV also have equal lengths. The perimeter of the parallelogram is `2(4)+2(ST)`. So `2(4)+2(ST)=14, 8+2(ST)=14, (ST)=6`, and ST = 3. Drop a perpendicular line from point T to SV that meets side SV at point P.

Since point P is on segment SV, the y - coordinate of point P is also 2. Then the y - coordinate of point T is equal to 2 plus the length of TP. Now sin `39^(@)=(TP)/(ST)`. Since `ST = 3, sin 39^(@)=(TP)/(3)`, so `TP = 3 sin 90^(@)`.
The y - coordinate of T is `2 + 3 sin 39^(@) ~~ 3.89`.