Question 1087321
1. What can be said of points lying on the line through the origin, bisecting the 1st and 3rd quadrant? 
<pre>
{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
line(-11,-11,11,11), 

circle(1,1,.1), locate(1,1,"(1,1)"), 

circle(2,2,.1), locate(2,2,"(2,2)"), 
circle(3,3,.1), locate(3,3,"(3,3)"), 
circle(4,4,.1), locate(4,4,"(4,4)"), 
circle(5,5,.1), locate(5,5,"(5,5)"), 
circle(6,6,.1), locate(6,6,"(6,6)"), 
circle(7,7,.1), locate(7,7,"(7,7)"), 
circle(8,8,.1), locate(8,8,"(8,8)"), 
circle(9,9,.1), locate(9,9,"(9,9)"), 
circle(10,10,.1), locate(10,10,"(10,10)"), 

circle(-1,-1,.1), locate(-1,-1,"(-1,-1)"), 
circle(-2,-2,.1), locate(-2,-2,"(-2,-2)"), 
circle(-3,-3,.1), locate(-3,-3,"(-3,-3)"), 
circle(-4,-4,.1), locate(-4,-4,"(-4,-4)"), 
circle(-5,-5,.1), locate(-5,-5,"(-5,-5)"), 
circle(-6,-6,.1), locate(-6,-6,"(-6,-6)"), 
circle(-7,-7,.1), locate(-7,-7,"(-7,-7)"), 
circle(-8,-8,.1), locate(-8,-8,"(-8,-8)"), 
circle(-9,-9,.1), locate(-9,-9,"(-9,-9)"), 
circle(-10,-10,.1), locate(-10,-10,"(-10,-10)") 


 )}}} 

Every point has the same x- and y- coordinates
</pre>
On the line bisecting the 2nd and 4th quadrant?
<pre>
{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
line(11,-11,-11,11), 

circle(-1,1,.1), locate(-1,1,"(-1,1)"), 

circle(-2,2,.1), locate(-2,2,"(-2,2)"), 
circle(-3,3,.1), locate(-3,3,"(-3,3)"), 
circle(-4,4,.1), locate(-4,4,"(-4,4)"), 
circle(-5,5,.1), locate(-5,5,"(-5,5)"), 
circle(-6,6,.1), locate(-6,6,"(-6,6)"), 
circle(-7,7,.1), locate(-7,7,"(-7,7)"), 
circle(-8,8,.1), locate(-8,8,"(-8,8)"), 
circle(-9,9,.1), locate(-9,9,"(-9,9)"), 
circle(-10,10,.1), locate(-10,10,"(-10,10)"), 

circle(1,-1,.1), locate(1,-1,"(1,-1)"), 
circle(2,-2,.1), locate(2,-2,"(2,-2)"), 
circle(3,-3,.1), locate(3,-3,"(3,-3)"), 
circle(4,-4,.1), locate(4,-4,"(4,-4)"), 
circle(5,-5,.1), locate(5,-5,"(5,-5)"), 
circle(6,-6,.1), locate(6,-6,"(6,-6)"), 
circle(7,-7,.1), locate(7,-7,"(7,-7)"), 
circle(8,-8,.1), locate(8,-8,"(8,-8)"), 
circle(9,-9,.1), locate(9,-9,"(9,-9)"), 
circle(10,-10,.1), locate(10,-10,"(10,-10)") 


 )}}}

The x- and y- coordinates of every point have the same absolute
value but opposite signs.
</pre>
2. What do points on the line parallel to the X axis,
   5 units above it, have in common?
<pre>
{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
line(-11,5,11,5), 

circle(1,5,.1),  

circle(2,5,.1),  
circle(3,5,.1), locate(3,6,"(4,5)"), 
circle(4,5,.1), locate(4,5,"(5,5)"), 
circle(5,5,.1), locate(5,6,"(6,5)"), 
circle(6,5,.1), locate(6,5,"(7,5)"), 
circle(7,5,.1), locate(7,6,"(8,5)"), 
circle(8,5,.1), locate(8,5,"(9,5)"), 
circle(9,5,.1), locate(9,6,"(10,5)"), 
circle(10,5,.1), locate(10,5,"(11,5)"), 

circle(-1,5,.1), locate(-1,6,"(-1,5)"), 
circle(-2,5,.1), 
circle(-3,5,.1),  
circle(-4,5,.1), locate(-4,5,"(-3,5)"), 
circle(-5,5,.1), locate(-5,6,"(-4,5)"), 
circle(-6,5,.1),  
circle(-8,5,.1), locate(-7,6,"(-6,5)"), 
circle(-8,5,.1),  
circle(-9,5,.1),  
circle(-10,5,.1), locate(-10,5,"(-8,-10)") 


 )}}}

All the points have the same y-coordinates, they are all 5.
</pre>
3. What do points on the line parallel to the Y axis and 3 units to the left of it have in common?
<pre>
{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
line(-3,-11,-3,11), 

circle(-3,1,.1), locate(-3,1,"(-3,1)"), 

circle(-3,2,.1), locate(-3,2,"(-3,2)"), 
circle(-3,3,.1), locate(-3,3,"(-3,3)"), 
circle(-3,4,.1), locate(-3,4,"(-3,4)"), 
circle(-3,5,.1), locate(-3,5,"(-3,5)"), 
circle(-3,6,.1), locate(-3,6,"(-3,6)"), 
circle(-3,7,.1), locate(-3,7,"(-3,7)"), 
circle(-3,8,.1), locate(-3,8,"(-3,8)"), 
circle(-3,9,.1), locate(-3,9,"(-3,9)"), 
circle(-3,10,.1), locate(-3,10,"(-3,10)"), 

circle(-3,-1,.1), locate(-6,-1,"(-3,-1)"), 
circle(-3,-2,.1), locate(-6,-2,"(-3,-2)"), 
circle(-3,-3,.1), locate(-6,-3,"(-3,-3)"), 
circle(-3,-4,.1), locate(-6,-4,"(-3,-4)"), 
circle(-3,-5,.1), locate(-6,-5,"(-3,-5)"), 
circle(-3,-6,.1), locate(-6,-6,"(-3,-6)"), 
circle(-3,-7,.1), locate(-6,-7,"(-3,-7)"), 
circle(-3,-8,.1), locate(-6,-8,"(-3,-8)"), 
circle(-3,-9,.1), locate(-6,-9,"(-3,-9)"), 
circle(-3,-10,.1), locate(-6,-10,"(-3,-10)") 


 )}}}

All the points have the same x-coordinates, they are all -3.
</pre> 
4. What is the distance from the X axis to (7,-2)? 
<pre>
We draw a line straight to the X axis from (7,-2)

{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
line(7,-2,7,0), 

circle(7,-2,.15),locate(7,-2,"(7,-2)") )}}} 

The line is 2 units long, so the distance to the X-axis is 2.
</pre>
From the Y axis? 
<pre>
We draw a line straight to the Y axis from (7,-2)


{{{drawing(400,400,-10,10,-10,10, graph(400,400,-10,10,-10,10),
line(7,-2,0,-2), 

circle(7,-2,.15),locate(7,-2,"(7,-2)") )}}} 

The line is 7 units long, so the distance to the Y-axis is 7.

Edwin</pre>