Area of a triangle:


1/2 * [x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2)]

where (x1,y1), (x2,y2) and (x3,y3) are 3 end-points of a triangle.

If the origin (0,0) shifts to a point (h,k),

then old co-ordinates of point P(x,y) changes to (x-h, y-k)

If (x1,y1), (x2,y2), (x3,y3) and (x4,y) are the vertices of a PARALLELOGRAM,

then

x1+x3 = x2+x4 AND
y1+y3 = y2+y4

To prove end-points A,B,C, and D are the vertices of:

i. A PARALLELOGRAM:
* Show that diagonals AC and BD bisect each other.

ii. A RHOMBUS:
* Show that diagonals AC and BD bisect each other.
* Show that a pair of adjacent sides are equal.

iii. A SQUARE:
* Show that diagonals AC and BD bisect each other.
* Show that a pair of adjacent sides are equal.
* Show that two diagonals AC and BD are equal.

iv. A RECTANGLE:
* Show that diagonals AC and BD bisect each other.
* Show that two diagonals AC and BD are equal.

Dear Pradeep bhai,

wonderful Job!! One more thanks frm me....!! I am looking for Probabilty & P&C notes..Plz do post them with some examples.

Thanks a lot Pradeep. You rock!!!
I truly appreciate your work.

Thanks Govardhan and sanabk..!

I don't have any flashcard for Probability and P&C. I didn't bother to spend too much time on those topics and record flashcards. Even in the real gmat, i just got 1 question.

I would suggest that you go through Stuart's posts on Probability in this forum. He helped me understand the technique that i never used to be comfortable with earlier. Good luck!

SLOPE +ve OR -ve:


Slope is tan x
where, x is angle of inclination.

i. Slope is POSITIVE when x is acute.
ii. Slope is NEGATIVE when x is obtuse.

Finding Slope:


Slope can be calculated in 2 ways,

i. m = y1-y2 / x1-x2

ii. m = - Coeff. of x / coeff. of y (OR)
m = -a / b
[From ax + by + c = 0]

If two lines l1 and l2 are PARALLEL, then m1 = m2 ....... [Where, m1 and m2 are the slopes of lines l1 and l2 respectively]

If two lines l1 and l2 are PERPENDICULAR, then m1 * m2 = -1....... [Where, m1 and m2 are the slopes of lines l1 and l2 respectively]

Slope of all HORIZONTAL LINES is 0..... [Lines parallel to x-axis]

Slope of all VERTICAL LINES is undefined..... [Lines parallel to y-axis. Angle of inclination of ANY line parallel to y-axis is 90 or 270 degrees]

Finding EQUATION of a LINE:


i. PASSING through two points (x1,y1) and (x2,y2):
y-y1 / y2-y1 = x-x1 / x2-x1

ii. y = mx+c, when slope (m) and y-intercept (c) are given.

iii. y-y1 = m*(x-x1), when slope (m) and one of the points (x1,y1) on the line are given.

iv. x/a + y/b = 1, when x-intercept (a) and y-intercept (b) are given.

Angle of inclination b/w 2 SLOPES:


Angle (x) between two slopes, tan x = |(m1-m2) / (1+m1*m2)|

Length of perpendicular from point (x1,y1) to the line ax+by+c = 0 is

|ax1+by1+c / root(a^2+b^2)|

Distance between two lines [PARALLEL lines] ax+by+c1 = 0 and ax+by+c2 = 0 is

|c1-c2 / root(a^2+b^2)|