Step by step
The question
Question: which quadrant is (−4, 1) in?
(−4, 1)
1 Read the signs
The first number is x.
−4 is negative.
So the point is left of the y-axis.
x = −4 → −
The second number is y.
1 is positive.
So the point is above the x-axis.
y = 1 → +
2 Name the quadrants
Draw the grid.
The two axes cut it into four parts.
Each part is called a quadrant.
3 Find the quadrant
Left and up: (−, +).
That is quadrant Ⅱ.
= (−, +) → quadrant II
Careful!
We count against the clock.
Ⅱ is the top left.
Counting the other way swaps Ⅱ and Ⅳ.
Careful: not quadrant IV ✗
4 Check
Let's check: plot it.
From 0, go left 4.
Then go up 1.
Put a dot.
The dot is in quadrant Ⅱ.
So the answer is right!
Let's look back.
First: read the signs.
Then: name the quadrants.
Then: find the quadrant.
Last: check.
Answer
Careful: not quadrant IV ✗