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- Distance between two points P(x
_{1},y_{1}) and Q(x_{2},y_{2}) is given by = - If a point R (x,y) divides P(x
_{1},y_{1}) and Q(x_{2},y_{2}) 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(x
_{1},y_{1}) and Q(x_{2},y_{2}) 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(x
_{1},y_{1}) and Q(x_{2},y_{2}) in the ratio of y_{1}: y_{2} - The Y axis divides the line joining P(x
_{1},y_{1}) and Q(x_{2},y_{2}) in the ratio of x_{1}: x_{2}

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 (x_{1},y_{1}) and Q(x_{2},y_{2}), 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 x_{1},y1

⇒ y – y_{1} = m(x – x_{1})

**Two Point Form:** Two points are x_{1},y_{1} and x_{2},y_{2}

⇒

**Two Intercept Form:** X-intercept is a, Y-intercept is b.

⇒ OR bx + ay = ab

A cute angle between two lines with slope m_{1} and m_{2} is given by

⇒

⇒ For parallel lines, θ = 0°; m_{1} = m_{2}

⇒ For parallel lines, θ = 90°; m_{1}m_{2} = -1

Distance of a point P (x_{1},y_{1}) from a line ax + by + c = 0

⇒

⇒ From origin, d =

Distance between two parallel lines, ax + by + c_{1} = 0 and ax + by + c_{2} = 0

⇒

**EduRev's Tip:** If we know three points A(x_{1},y_{1}), B(x_{2},y_{2} ) and C(x_{2},y_{2}) of a parallelogram, the fourth point is given by

⇒ (x_{1} + x_{3} – x_{2}, y_{1} + y_{3} – y_{2})

**Triangle**

The vertices are P (x_{1},y_{1}), Q(x_{2},y_{2}) and R(x_{3},y_{3})

Incenter

Centroid =

Area = ½ [ x_{1}(y_{2} – y_{3}) + x_{2} (y_{3} – y_{1}) + x_{3} (y_{1} – y_{2})]

**Circle**

General Equation: x^{2} + y^{2} + 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

⇒ x^{2} + y^{2} = r^{2}

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