Class 10 Maths · Chapter 7 · Topic 1 of 4
Read a point as across, then up or down
Coordinates are directed moves; distances are non-negative.
Ideas you’ll use
- Coordinates
- (x, y) is an ordered pair: x is the signed horizontal position and y is the signed vertical position. The origin is (0, 0).
Understand it, one idea at a time
Choose an idea. Follow its reason, calculation and clue in the picture.
Signs and coordinate order
y-coordinate (unit)
x-coordinate (unit)
Equal units on both axes.
- Two points · Original coordinate construction.
- 1. A: left 2, up 3 · (-2, 3)
- 2. B: right 3, down 2 · (3, -2)
Assumptions: Both axes use the same length per unit. Straight segments join the stated coordinates. The algebra gives exact lengths.
Read the plotted values
Two points
| x-coordinate (unit) | y-coordinate (unit) |
|---|---|
| -2 | 3 |
| 3 | -2 |
Signed coordinates describe position; distances to axes use absolute values.
Move horizontally first
For (−2,3), the x entry sends you two units left.
x=−2In the picture: Follow the horizontal direction from the origin.
Read all the reasoning together
Move horizontally first
For (−2,3), the x entry sends you two units left.
x=−2Move vertically second
The y entry sends you three units up.
y=3Separate distance from sign
Distances to axes use absolute values.
distance to y-axis=2; to x-axis=3Keep order and axis rules
Swapping entries changes the point. On an axis one coordinate is zero.
x-axis: y=0; y-axis: x=0
Coordinates are directed moves; distances are non-negative.
Worked example: Order matters
A(−2, 3) and B(3,−2) are different pointsDo not swap the entries. The distance from A to the y-axis is |−2| = 2 units, and to the x-axis is |3| = 3 units.
Read the supporting explanation
For (−2, 3), move 2 units left and 3 up. Its x-coordinate is negative, even though its distance from the y-axis is positive. Points on the x-axis have y = 0; on the y-axis they have x = 0.
Go deeper: Coordinate and distance are different
Coordinates can be negative. Distances cannot. The sign records direction; the absolute value records distance to the corresponding axis.
Your turn
Try the idea yourself. Show your reasoning, then compare.
Question
Which axis contains (0, −5)? What is its distance from the origin?
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