Coordinate Geometry, plotted point by point.
Read the concepts, practice all 160 questions with hints and instant feedback, race the clock in Quiz Mode, or play a game. Click the grid to plot points — click more than once and they'll join up automatically.
x = abscissa · y = ordinate · clear points
- Cartesian plane Two perpendicular number lines — a horizontal x-axis and a vertical y-axis — used together to fix the position of any point.
- Origin The point (0, 0) where the x-axis and y-axis cross.
- Abscissa The x-coordinate of a point — its distance from the y-axis.
- Ordinate The y-coordinate of a point — its distance from the x-axis.
- Quadrants The axes split the plane into four regions. I: (+,+) · II: (−,+) · III: (−,−) · IV: (+,−).
- On an axis A point on the x-axis has ordinate 0. A point on the y-axis has abscissa 0. The origin lies in no quadrant.
Important Formulas
Concept Card
For P(5, 3): abscissa is 5, ordinate is 3. Quadrant I, since both are positive.
On the x-axis, points look like (x, 0). On the y-axis, points look like (0, y).
Worked Examples
Straight Lines & Slope
- Slope (m) How steep a line is: m = (y₂−y₁)/(x₂−x₁). Positive slope rises left→right; negative falls; zero is horizontal; a vertical line has no defined slope.
- Slope-intercept form A line can be written y = mx + c, where m is the slope and c is the y-intercept.
- x- & y-intercepts The x-intercept is where a line crosses the x-axis (y = 0); the y-intercept is where it crosses the y-axis (x = 0).
- Parallel lines Two lines are parallel exactly when their slopes are equal: m₁ = m₂.
- Perpendicular lines Two lines are perpendicular exactly when their slopes multiply to −1: m₁ · m₂ = −1.
- Collinearity by slope Three points are collinear if the slope between any two pairs of them is the same.
Section Formula
More Worked Examples
Explore: Distance & Midpoint — drag the points!
- Drag the gold point A or the teal point B anywhere on the grid (click/tap-and-drag; works on touch too).
- The dashed gold and teal legs are the horizontal and vertical gaps — count the squares yourself, then check against the numbers below.
- The violet diamond is the midpoint M — it updates live as you move A or B.
Head to Practice Mode for all 160 questions with hints, or jump into a timed Quiz, or try a Game.
๐ Timed Challenge
15 seconds per question · +4 correct · −1 wrong · 3 lives
Topic How many questions?๐ Shift & Reflect
Translations (slides), reflections and symmetry — the grid shows the working, not just the answer.
- Pick a move above — Translate, or a Reflect option.
- C is the point you're shown already moved; D is the point you must move yourself.
- Work out where D lands, then type its new x and y into the boxes and hit Check.
- Stuck? Tap ๐ Show me on the grid — it draws the guide lines (arrows for a slide, the mirror line for a reflection) so you can see exactly how D became D′.
- Tap New Question → whenever you're ready for another.
๐ Plot the Point
๐ฏ Coordinate Guess
Type the coordinates of the plotted point.
๐ฑ️ Drag & Drop
Drag the chip onto the point on the grid.
๐ Distance Finder
Two points are marked. Work out the distance between them using the distance formula.
๐ Midpoint Finder
Find the midpoint of the segment joining the two marked points.
➗ Bisect & Trisect
Find the point that divides segment AB in the stated ratio (the section formula).
✖️ Line Crossing
Two straight lines are shown. Solve the pair of linear equations to find where they cross.
๐ Slope & Y-Intercept
A straight line y = mx + c is drawn. Read its slope and y-intercept off the grid.
๐งฉ Match Columns
Click a term, then its matching definition.
