Question

what is distance formula , section formula ans midpoint formula..
plz tell me
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Answer 1

$\underline{\bigstar\:\textsf{Distance Formula\; :}}$

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

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

⠀

$\underline{\bigstar\:\textsf{Section Formula\; :}}$

• Section Formula is used to find the co ordinates of the point(Q) Which divides the line segment joining the points (B) and (C) internally or externally.

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

⠀

$\underline{\bigstar\:\textsf{Mid Point Formula\; :}}$

• Mid Point formula is used to find the Mid points on any line.

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

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Answer 2

$\large\underline\purple{\bold{Solution :- }}$

$\boxed{ \red{ \bf \: Distance \: Formula }}$

Let us consider a line segment joining the points A and B,

then distance between A and B is given by

$\: {\underline{\boxed {\blue{{\rm{\quad AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \quad}}}}}}$

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

$\boxed{ \blue{ \bf \: Section \: Formula}}$

Let us consider a line segment joining the points A and B,

and Let C (x, y) be any point which divides AB internally in the ratio m: n, then coordinates of C(x, y) is given by

$\boxed{ \green{\rm \:( x, y) = (\dfrac{mx_2 + nx_1}{m + n} , \dfrac{my_2 + ny_1}{m + n} )}}$

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

$\boxed{ \purple{ \bf \: Midpoint \: Formula}}$

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(x, y) is given by

$\boxed{ \pink{\rm \:( x, y) = (\dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} )}}$

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