Coordinate Geometry represents the geometric figures in a two-dimensional plane x-axis and y-axis (x,y)
This two axes of the coordinate plane are the horizontal x-axis and the vertical y-axis.
The coordinate axes divide the plane into four quadrants, and the point that intersect these axes is known as origin (0, 0). Further, any point in the coordinate plane is referred to by a point (x, y), where the x value is the position of the point with reference to the x-axis, and the y value is the position of the point with reference to the y-axis.
In first quadrant, x & y both are positive. (+ , +)
In second quadrant, x is negative and y is positive. (+ , -)
In third quadrant, x is negative and y is negative. (- , -)
In fourth quadrant, x is positive and y is negative. (+ , -)
A straight line is a shortest distance between two distinct points.
Equation of a straight line is : y = mx + c
Here x & y are variables. c is constant or you can say Y-intercept which passes through Y-aixs. m is a slope of the line
Distance Formula 1 : Distance from a point from an origin (0,0)
Distance Formula 2 : Distance between two points (other than origin)
Example : If the point (k,3) is at a distance of √5 units from the point (2,k), then find k.
What will be the value of k if the distance between (k,-4) and (-8,2) be 10?
Prove that (3,2), (5,4), (3,6), (1,4) are the vertices of a square
Prove that the triangle with vertices at the points (0,3), (-2,1), and (-1,4) is right angled.
The points A(2,3/2), B(-3,-7/2), C(k,9/2) are collinear, then find the value of k.
Section Formula : Internal & External Division
Find the coordinates of the point which divides the points A(-7,4) and B(8,9) internally in the ratio 2:3
Find the coordinate of the point which divides externally the join of the pair of the points A(1,-2) and B(4,7) in the ratio of 2:3
Find the in which the points C(-1,-1) divides the join of points A(3,3) and B(7,7)
In what ratio is the segment joining the pair of the points A(2,-4) and B(-3,6) is divided by the x-axis, also find coordinate on x-axis
Area of Triangle
Find the area of triangle whose vertices are A(2,-1), B(-3,-4) and C(0,2)
Straight Line and Types of line
Types of straight line equation : Slope Intercept form
Find the equation of a straight line having slope 2 and making intercept on y-axis at (0,2)
Find the slope of line passing through the points A(4,7) and B(1,-2)
Find the equation of straight line passing through the origin and having slope 2
Types of straight line equation : Slope Point Form and Two Point Form
Types of straight line equation : Two Intercept Form
Find the equation of a straight line having intercept 2 and 3 on the coordinate axis.
Find the equation of a straight line passing through the point (5,3) and making an equal intercept of opposite sign on the axis
Find the equation of straight line passing through the point (3,4) such that the sum of its intercepts on the axis is 14
Find the slope and the intercept of the line 2x – 3y = 6
Find the slope and the intercept of the line 6x – 5y – 1 = 0
