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Important Formulas for CAT Coordinate Geometry


  • Distance between two points P(x1,y1) and Q(x2,y2) is given by = Important Formulas for CAT Coordinate Geometry
  • If a point R (x,y) divides P(x1,y1) and Q(x2,y2) internally in the ratio of m:n, the coordinates of R ie (x,y) are given by Important Formulas for CAT Coordinate Geometry
  • If a point R (x,y) divides P(x1,y1) and Q(x2,y2) externally in the ratio of m:n, the coordinates of R ie (x,y) are given by Important Formulas for CAT Coordinate Geometry

EduRev's Tip:

  •  The X axis divides the line joining P(x1,y1) and Q(x2,y2) in the ratio of y1 : y2
  • The Y axis divides the line joining P(x1,y1) and Q(x2,y2) in the ratio of x1 : x2 

Slope(m) of a line is the tangent of the angle made by the line with the positive direction of the X-Axis.
For a general equation ax + by + c = 0; slope (m) = -a/b.
For a line joining two points, P (x1,y1) and Q(x2,y2), the slope(m) is = Important Formulas for CAT Coordinate Geometry
Important Formulas for CAT Coordinate Geometry
Equation of a line parallel to X-axis is y = a {Of X-Axis is y = 0}
Equation of a line parallel to Y-Axis is x = a {Of Y-Axis is x = 0}
The intercept of a line is the distance between the point where it cuts the X-Axis or Y-Axis and the origin. Y-Intercept is often denoted with the letter ‘c’.

Equation of a line
General form: ax + by + c = 0

Slope Intercept Form: Slope is m, y-intercept is c
⇒ y = mx + c

Slope Point Form: Slope is m, point is x1,y1
⇒ y – y1 = m(x – x1)

Two Point Form: Two points are x1,y1 and x2,y2
Important Formulas for CAT Coordinate Geometry

Two Intercept Form: X-intercept is a, Y-intercept is b.
Important Formulas for CAT Coordinate Geometry OR bx + ay = ab
A cute angle between two lines with slope m1 and m2 is given by
Important Formulas for CAT Coordinate Geometry
⇒ For parallel lines, θ = 0°;  m1 = m2
⇒ For parallel lines, θ = 90°; m1m2 = -1
Distance of a point P (x1,y1) from a line ax + by + c = 0
Important Formulas for CAT Coordinate Geometry
⇒ From origin, d = Important Formulas for CAT Coordinate Geometry

Distance between two parallel lines, ax + by + c1 = 0 and ax + by + c2 = 0
Important Formulas for CAT Coordinate Geometry

EduRev's Tip: If we know three points A(x1,y1), B(x2,y2 ) and C(x2,y2)  of a parallelogram, the fourth point is given by
⇒ (x1 + x3 – x2, y1 + y3 – y2)

Triangle
Important Formulas for CAT Coordinate Geometry
The vertices are P (x1,y1), Q(x2,y2) and R(x3,y3)
Incenter Important Formulas for CAT Coordinate Geometry
Centroid = Important Formulas for CAT Coordinate Geometry
Area = ½ [ x1(y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)] 

Circle
General Equation: x2 + y2 + 2gx + 2fy + c = 0
⇒ Centre is (-g, -f) and radius = Important Formulas for CAT Coordinate Geometry
Centre is (h, k) and radius is r
Important Formulas for CAT Coordinate Geometry
Centre is origin and radius is r
⇒ x2 + y2 = r2

The document Important Formulas for CAT Coordinate Geometry is a part of the CAT Course Quantitative Aptitude (Quant).
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FAQs on Important Formulas for CAT Coordinate Geometry

1. What are the formulas for finding the distance between two points in coordinate geometry?
Ans. The formula for finding the distance between two points (x1, y1) and (x2, y2) in coordinate geometry is given by: Distance = √((x2 - x1)^2 + (y2 - y1)^2)
2. How do I find the midpoint of a line segment in coordinate geometry?
Ans. To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), you can use the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
3. What is the formula for finding the slope of a line in coordinate geometry?
Ans. The formula for finding the slope of a line passing through two points (x1, y1) and (x2, y2) is given by: Slope = (y2 - y1)/(x2 - x1)
4. How can I determine if three points in coordinate geometry are collinear?
Ans. To determine if three points (x1, y1), (x2, y2), and (x3, y3) are collinear, you can calculate the slopes of the line formed by the first two points and the line formed by the second two points. If both slopes are equal, then the three points are collinear.
5. What is the formula for finding the equation of a straight line in coordinate geometry?
Ans. The formula for finding the equation of a straight line passing through a point (x1, y1) with slope m is given by: y - y1 = m(x - x1)
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