Step 1 of 10
Start
A sign tells the direction.
Variable coordinates
(a, b), (−a,b), (a,−b), (−a,−b)
(3,y) is below and right of (x,−1)
For (a,b), what do the signs say?
R: left 5, down 2 | k is below −1
Read slots
Move
Mirror
Compare
Sign Plotter
Two-slot coordinate reader
Let a = 4 and b = 3. Both are positive distances.
First slot · x
+a = +4
right 4
( , )
Second slot · y
+b = +3
up 3
First slot: + means right
Second slot: + means up
(+a,+b) = (4,3)
Flip x sign · reflect across y-axis
(a,b) → (−a,b)
Flip y sign · reflect across x-axis
(+a, +b) = (4,3)
(−a, +b) = (−4,3)
(+a, −b) = (4,−3)
(−a, −b) = (−4,−3)
Position becomes an inequality
Only compare matching coordinate slots.
Right compares first coordinates
3 > x
Below compares second coordinates
y < −1
Same fact: −1 > y
The same sign map predicts results
Quadrants record the signs of a and b.
Same signs → positive
Quadrant II
(−, +)
a×b negative
a÷b negative
a÷b negative
Quadrant I
(+, +)
a×b positive
a÷b positive
a÷b positive
Quadrant III
(−, −)
a×b positive
a÷b positive
a÷b positive
Quadrant IV
(+, −)
a×b negative
a÷b negative
a÷b negative
Opposite signs → negative
On an axis, one coordinate is zero
a×b = 0either coordinate is 0
a÷ba=0 gives 0 if b≠0
b=0 is undefined
b=0 is undefined
Your turn
Use each coordinate slot once.
k is below −1, so k ___ −1
Plot R. Then compare k.
Show both answers.
Plot R and compare k with −1.
Nice work!
First slot: left → negative
Second slot: down → negative
R = (−5, −2)
Below → smaller y-value
k < −1
Signs place the point.
✓
Signs mapped!
Each slot controls one direction.
1 · Readx slot first
y slot second
y slot second
2 · Movesign gives
direction
direction
3 · Comparematch x with x
y with y
y with y