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