<p>Hi, I just wanted to say thanks again to everyone who has been helping me with these math questions. I have been seeing a dramatic improvement! I average about only 1-2 Wrong per section. </p>
<p>I got everything right in this section, but omitted this one</p>
<p>8.) Points P, Q, R, S, T, and U are all different points lying in the same plane. Points P, Q, and U lie on the same line. The line though points P and Q is perpendicular to the line through points R and S. The line though points R and S is perpendicular to the line through points T and U. Which of the following sets containts points that must lie on the same line?
A. P, Q, R
B. Q, R, S
C. Q, R, T
D. Q, T, U
E. R, T, U</p>
<p>Thanks!</p>
<p>Congratulations on your improvement!</p>
<p>For this problem, I would draw a diagram.</p>
<p>First, draw a line with P, Q, and U on the same line. Then draw a perpendicular line through your first line, and label points R and S on this new line (on opposite sides of your first line for simplicity). </p>
<p>Here comes the trickier part. Notice that it says that the line through R and S is perpendicular to 2 lines. If 2 lines are perpendicular to the same line, then they must be parallel to each other. Also notice that the 2nd line it says line RS is perpendicular has point U on it. This is also on the first line we drew (PQU). </p>
<p>If a line is parallel to another line, and they have a point in common (U), then they have to be the same line. This reveals that T is also on the line PQU. The only choice with 3 out of 4 of TPQU is D. That is the answer.</p>
<p>Notice all answers but one has R in it. You can automatically knock out everyone with R or S because you know that you can't tell which is on the line or not.</p>