Question 409643
In the diagram, three vertices of parallelogram ORST are O(0, 0), R(b, d), and T(a,0).  What are the coordinates of S?
<pre><font face = "batangche" color = "indigo" size = 4><b>
{{{drawing(400,300,-1,10,-1,10,
 locate(.4,.7,"O(0,0)"),locate(7.4,.7,"T(a,0)"),
locate(.7,5.5,"R(b,d)"), circle(7,0,.08), circle(7,0,.05),
red(line(-2,0,11,0), line(0,-2,0,11)), line(0,0,2,5),
locate(9.8,0,x), locate(-.3,10,y)



 )}}}

Since T is <u>a</u> units to the right of O, then S must be <u>a</u> units to the
right of R.  R is <u>b</u> units to the right of the y-axis, so S must be
<u>a</u> more units to the right of the y-axis than R is, so S's x-coordinate
must be <u>a</u> more than R's x-coordinate, so we add <u>b</u> to R's x-coordinate
and get that S's x-coordinate is <u>b+a</u>.  Also S must be the same distance
above the x-axis as R is.  R is <u>d</u> units above the x-axis, so S's 
y-coordinate must be the same as R's y-coordinate, <u>d</u>.  So the coordinates
of point S are S(b+a,d).

{{{drawing(400,300,-1,10,-1,10,
line(7,0,9,5), locate(.4,.7,"O(0,0)"),locate(7.4,.7,"T(a,0)"),
locate(.7,5.5,"R(b,d)"),locate(8.4,5.7,"S(b+a,d)"),
red(line(-2,0,11,0), line(0,-2,0,11)), line(0,0,2,5), line(2,5,9,5),
locate(9.8,0,x), locate(-.3,10,y)

 )}}}

Since <u>b+a</u> is the same as <u>a+b</u>, the correct choice is 3.

Edwin</pre>