Co-ordinate Geometry — Class 10 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Co-ordinate Geometry, written for Class 10 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Co-ordinate Geometry in one look
points become number pairs, so distance, division and slope all turn into arithmetic
The plane, and how a point is named
- two perpendicular number lines meet at the origin O(0, 0), the horizontal one called the X axis and the vertical one the Y axis
- a point is written as an ordered pair (x, y), the x co-ordinate always first, and (3, 5) is a different point from (5, 3)
- x is the distance from the Y axis and y the distance from the X axis, each carried with its sign
- the two axes cut the plane into four quadrants, numbered anticlockwise starting from the upper part on the side where both are positive
- a point on the X axis has y = 0, and a point on the Y axis has x = 0, which is how such conditions are turned into equations
The four formulas the chapter runs on
- distance between two points
d = √(x_2-x_1)^2 + (y_2-y_1)^2 - midpoint of the segment joining them
M = left(x_1+x_2/2, y_1+y_2/2right) - point dividing the segment in the ratio m:n
P = left(mx_2+nx_1/m+n, my_2+ny_1/m+nright) - centroid of a triangle from its vertices
G = left(x_1+x_2+x_3/3, y_1+y_2+y_3/3right) - slope of the line through two points
m = y_2-y_1/x_2-x_1
Why the distance formula is the Pythagoras theorem
- join the two points and complete a right angled triangle with one side horizontal and one vertical
- the horizontal side has length |x_2 - x_1| and the vertical side |y_2 - y_1|
- the segment joining the points is the hypotenuse of that triangle
- applying a^2 + b^2 = c^2 and taking the square root gives the formula exactly
- because both differences are squared, the order of the two points does not matter and the distance is never negative
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Co-ordinate Geometry sheet covers
- Cartesian co-ordinates
- Quadrants
- The plane, and how a point is named
- The four formulas the chapter runs on
- distance between two points
- midpoint of the segment joining them
- point dividing the segment in the ratio m:n
- centroid of a triangle from its vertices
- slope of the line through two points
- Why the distance formula is the Pythagoras theorem
- Distance, and using it to identify a shape
- What each squared distance test proves
- Section formula
- Division of a segment
- Using the section formula in the two directions
- Finding the ratio from a known point
- Slope of a line
- Parallel and perpendicular lines
- Slope, and what it tells you about two lines
- Reading a slope at a glance
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Co-ordinate Geometry the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.