Free Online Preparation for CAT with Minglebox e-CAT Prep. Cover basic concepts of Co-ordinate Geometry under Quantitative Aptitude for MBA Entrance Exam Preparation with Study material, solved examples and tests prepared by CAT coaching experts.
In two dimensional Coordinate Geometry, location of any point lying in the plane, is given by specifying the perpendicular distances of the point, from a set of fixed mutually perpendicular lines. The fixed mutually perpendicular lines are known as X-axes and Y-axes respectively. The point of intersection is known as the origin 'O'.
These 2 lines divide the given plane in 4 parts known as quadrants. Distances measured to the right hand side of origin O are treated as positive and distances measured towards the left of origin are treated as negative. In a similar way distances measured along the Y-axis and above the X-axis are treated as positive distance measured below the X-axis are treated as positive distances measured below the X-axis are treated as negative.
The Coordinates of a point are specified as an ordered pair, Comprising of its distance measured along the X and Y axis . Distance measured along one X-axis from the origin is known as abscissa, and usually denoted X, the G distance measured along the Y-axis From the origin is called the ordinate of the point and is denoted by y. Thus coordinate is of a point are specified as (x,y) I.e as (abscissa, ordinate).
The 4 quadrants are known as 1 st ,2 nd 3 rd & 4 th quadrant. The below diagram summarizes the sign of the abscissa and the ordinate of x points lying in 1 st , 2 nd , 3 rd , 4 th quadrant.
The distance d between 2 points and having coordinates
( ) and is given by
Section formula and mid point formula
The coordinates P of a point which divides the join of points and in the
ratio m:n is given by X = ; Y =
The Coordinates of the mid point of the line joining and is given by X =
; Y =
Coordinates of the centroid of a triangle
Let , and be the coordinates
of the vertices of triangle , then coordinates of it's centroid (x,y) is given by X =
; Y =
The coordinates of the incentre I (x,y) of the triangle with vertices ;
and side length a,b,c is given by X =
The area of triangle having vertices ; and is
given by = [ + + ]
Note – If area of is Zero points are collinear.
Condition for 4 points , no three of which are collinear to be a parallelogram . Let
, , be 4 points lying in a plane then , , , are the verticals of
a parallelogram if and
are the vertices of a square if in addition to above or
Slope of a line
The slope of a line is defined as tangent of the angle which the line makes in the positive direction of the x-axis in the anti – clockwise direction.
The slope is generally represented by 'm' thus in the notion used above
The equation of a line is given by y = mx+c where 'c' is the intercept mode on the y -axis by the line.
Equation of x-axis is y = 0
Equation of y-axis is x = 0
2 lines are said to be parallel if they have the same slope that is if where where m1 and m2 are the slopes of the 2lines.
2 lines said to be perpendicular if they product of there slope is -1. that is if then lines are perpendicular to each other. Different forms of the equation of a line.
Line passing through point and having slope 'm' .
Line passing through points and .
If a line makes intercept a,b on x and y-axis respectively then equation of line is given by
Angle between 2lines having slopes and is given by where is the actual
angle between the 2 lines.
Perpendicular distance between parallel lines , Let the equation of 2 lines be and line is given by
Perpendicular distance of a point from a line . Let be any point and let y = mx +c be any line, then the perpendicular distance of point p from line y = mx + c is given by
The equation of a circle having center at point (h,x) and radius 'r' given by
Find the equation of the line with slope 2 and intercept on the y-axis as -7 ?
we know that equation of the line having slope 'm' and intercept on y-axis is 'c' the equation is y = mx +c , hence equation of line is y = 2x – 7
The equation of a line which makes an intercept of 3 on x-axis and -3 on y-axis is
x – 2y = 5
x – 2y = 3
4x + 13y = 7
none of these
The line with the x-axis at point (3,0) and y-axis at the point (0,-3) hence equation of line is using
y = x-3 or x – y = 3
hence answer is option (2)
Find the equation of the line perpendicular to the line x + y = 2 and passing through (1,2)
y = x + 3
y = x – 1
y = x + 1
y – x = 2
Let slope of required line be 'm' then slope of line x + y = 2 is '-1' for lines to be perpendicular the product of their slope should be '-1' hence we get
m = 1
using one point slope from the equation of we get required equation as
(y – 2) = 1. (x-1)
y = x + 1
Hence (3) is the answer.
The equation of the line through the intersection of the lines 2x + y = 3 and 3y – x + 2 = 0 and having slope -1/2 is
14y +5x +10 = 0
14y+7x-9 = 0
14y+7x-6 = 0
14y+7x+11 = 0
Equation of any line through the point of intersection of the given lines is of the form (2x+y-3) + (3y-x+2) = 0 where k is the constant to be determined , remaining we get
(3k+1)y + (2-k)x+2k-3 = 0,but slope of this line (given) solving we get k = 3/5
hence putting the value of k = 3/5 we get equation required line as 14y+7x-9 = 0
The coordinate of the verities of a triangle are
The Coordinate of the centroid of the triangle with vertical is given by X
= : Y =
Hence X = Y =
Therefore option (4) is the correct answer.