Question

what r the formulas from the chapter coordinate geometry class 10​

Answer 1

$\begin{gathered}\Large{\bold{{\underline{Formula \: - }}}}  \end{gathered}$

1. Distance Formula :-

Let us consider a line segment joining the points A and B, then distance between A and B, is given by

$\purple{\boxed{\bf\:AB =\sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2}}}}$

$\sf \: where \: coordinates \: of \: A \: and \: B \: are \: (x_1,y_1) \: and \: B(x_2,y_2)$

2. Midpoint Formula :-

Let us consider a line segment joining the points A and B and let C (x, y) be the midpoint of AB, then coordinates of C is

$\red{\boxed{ \quad\bf \:( x, y) = \bigg(\dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2} \bigg) \quad}}$

$\sf \: where \: coordinates \: of \: A \: and \: B \: are \: (x_1,y_1) \: and \: B(x_2,y_2)$

3. Section Formula :-

Let us consider a line segment joining the points A and B and let C (x, y) be the point on AB, which divides AB in the ration m : n respectively, then coordinates of C is

$\blue{\boxed{ \quad\bf \:( x, y) = \bigg(\dfrac{nx_1+mx_2}{m + n} , \dfrac{ny_1+my_2}{m + n} \bigg) \quad}}$

$\sf \: where \: coordinates \: of \: A \: and \: B \: are \: (x_1,y_1) \: and \: B(x_2,y_2)$

4. Area of triangle :-

Let us consider a triangle ABC having coordinates

$\sf \:\: A \: (x_1,y_1) \: ,\: B(x_2,y_2) \: and \: C(x_3,y_3) \: then \:$

$\green{\boxed{\bf\ Area =\dfrac{1}{2} \bigg|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) \bigg|}}$

5. Centroid of a triangle :-

Let us consider a triangle ABC having coordinates

$\sf \:\: A \: (x_1,y_1) \: ,\: B(x_2,y_2) \: and \: C(x_3,y_3) \: then \:$

Centroid of triangle ABC, G(x, y) is given by

$\red{\boxed{ \quad\bf \:( x, y) = \bigg(\dfrac{x_1+x_2 + x_3}{3} , \dfrac{y_1+y_2 + y_3}{3} \bigg) \quad}}$