Important Formulae: Coordinate Geometry

# Important Formulas for CAT Coordinate Geometry

• Distance between two points P(x1,y1) and Q(x2,y2) is given by =
• 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
• 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

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 =

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

Two Intercept Form: X-intercept is a, Y-intercept is b.
OR bx + ay = ab
A cute angle between two lines with slope m1 and m2 is given by

⇒ 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

⇒ From origin, d =

Distance between two parallel lines, ax + by + c1 = 0 and ax + by + c2 = 0

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

The vertices are P (x1,y1), Q(x2,y2) and R(x3,y3)
Incenter
Centroid =
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 =
Centre is (h, k) and radius is r

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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