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Class 10Mathematics Chapter 2 - Coordinate GeometryFormulas Needed Quality Answer Needed​

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★ CO – ORDINATE GEOMETRY FORMULAS —

I) Distance Formula

Distance formula is used to find the distance between TWO given Points.

{\underline{\boxed{\frak{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}}}}

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II) SECTION Formula

Section Formula is used to find the ratio(x, y) of the point (A) Which divides the line segment joining the points (B) and (C) internally or externally.

{\underline{\boxed{\frak{ \Big(x, y \Big) = \Bigg(\dfrac{mx_2 + nx_1}{m + n} \dfrac{my_2 + ny_1}{m + n}\Bigg)}}}}⠀

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III) Mid – point Formula

Mid Point formula is used to find the Mid points(x, y) on any line segment.

{\underline{\boxed{\frak{\Bigg(\dfrac{x_1 + x_2}{2} \; or\; \dfrac{y_1 + y_2}{2} \Bigg)}}}}

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IV) Trisection of Line Formula

To find the points of trisection A and B which divides the line segment joining the points

\sf Q(x_1, y_1) and \sf R (x_2, y_2) into THREE equal parts.

\underline{\boxed{\frak{A = \dfrac{x_2 + 2x_1}{3},\; \dfrac{y_2 + 2y_1}{3}\;\&\;B = \dfrac{2x_2 + x_1}{3},\; \dfrac{2y_2 + y_1}{3}}}}

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V) Centroid of Triangle

If \sf A(x_1, y_1), B(x_2, y_2) and \sf C(x_3, y_3) are the vertices of any ∆ ABC, then the co–ordinates of its centroid (Q) are given by.

\underline{\boxed{\frak{Q = \dfrac{x_1 + x_2 + x_3}{3}, \: \dfrac{y_1 + y_2 + y_3}{3}}}}

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VI) Area of Triangle

If the points A, B and C are the vertices of a Δ ABC, then the formula of area of triangle is given by.

\underline{\boxed{\frak{\triangle = \dfrac{1}{2} x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)}}}

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