The axes carry on past zero, so a point can be left of it, below it, or both.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
What the signs say
(−3, 5) is 3 to the left and 5 up. The signs give the directions.
Reflections change a sign
(3, 5) reflected across the vertical axis is (−3, 5). Only the first number flips.
Distance along a line
Points sharing a coordinate are easy: from (−2, 4) to (5, 4) is 7 across.
Four regions
With both axes extended into the negatives, the plane splits into four quadrants, numbered anticlockwise from the top right. Quadrant I has both coordinates positive; II has x negative and y positive; III has both negative; IV has x positive and y negative.
Signs tell you the quadrant
The point (−3, 5) has a negative x and a positive y, so it sits in Quadrant II. You can name the quadrant from the signs alone, without plotting anything. That is a quick check that a point has been plotted where you meant.
Reflections change signs
Reflecting (3, 5) across the y-axis gives (−3, 5); across the x-axis gives (3, −5). Reflecting across both gives (−3, −5). Each reflection flips the sign of one coordinate, which makes reflection something you can compute rather than only draw.
The order still matters
(−3, 5) and (5, −3) are different points in different quadrants. Extending into the negatives does not relax the convention that the first number is horizontal. If anything it matters more, since the sign now changes the region too.
Step 2: Try It Yourself
Tap and try it out.
Step 3: Watch an Example
One step at a time.
Watch Leo Find a Distance
Leo measures from (−4, 2) to (3, 2).
- Step 1
He notices both points have the same second coordinate, so the gap is horizontal.
Step 4: Your Turn
Practice makes it stick.
The Reflection
Problem 1 of 2
(6, −2) reflected across the vertical axis. What is the first coordinate?
The Gap
Problem 2 of 2
How far is it from (−5, 3) to (2, 3)?
Around the Grid
1 of 4
In (−4, −7), how far up or down do you go?
2 of 4
How far is it from (1, −3) to (1, 5)?
3 of 4
(2, 7) reflected across the horizontal axis. What is the second coordinate?
4 of 4
How far is it from (−6, 0) to (0, 0)?
Step 5: Quick Check
Show what you know.
Question 1 of 2
How far is it from (−3, 4) to (6, 4)?
Question 2 of 2
What does a negative first coordinate mean?
What You Learned
- The grid has four quadrants.
- The signs of the coordinates give the directions.
- Points sharing a coordinate are a straight distance apart.