Question

what is coordinate geometry ??
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itz shivani .. ​

Answer 1

$\pink \bigstar \: \: \: \: \underline{\textsf{\textbf{\color{blue}{What is Coordinate Geometry }}}}$

Coordinate Geometry is a part of geometry that uses two or more numbers to specify the position of any point, figure or object. The position of the object can be defined in a line or a plane or three dimensional space and so on. Below are the types of Coordinate System.

Additional information:

$\underline{\textsf{\textbf{\color{green}{1).Origin : }}}}$

This is any fixed point which is convenient to you. All measurements are taken w.r.t this fixed point.

$\underline{\textsf{\textbf{\color{yellow}{2).Axis or Axes : }}}}$

Any fixed direction passing through origin and convenient to you can be taken as axis. if the position of a point or position of all the points under consideration always happen to be in a particular direction, then only one axis is required

$\underline{\textsf{\textbf{\color{red}{3).Abscissa : }}}}$

• It lies on x- axis ( horizontal line )

$\underline{\textsf{\textbf{\color{purple}{4).Ordinate : }}}}$

• It lies on y - axis ( vertical line)

$\underline{\textsf{\textbf{\color{orange}{5).Cartesian plane is divided into four quadrants : }}}}$

Quadrant 1 :- (+x, +y)

➜ In Quadrant 1 both abscissa and ordinate are positive.

Quadrant 2 :- (-x, +y)

➜ In Quadrant 2 abscissa is negative and ordinate is positive.

Quadrant 3 :- (-x, -y)

➜ In Quadrant 3 abscissa is negative and ordinate is also negative.

Quadrant 4 :- (+x, -y)

➜ In Quadrant 4 abscissa is positive and ordinate is negative.

$\underline{\textsf{\textbf{\color{green}{7).Some formulasof coordinate geometry : }}}}$

1. Distance Formula :-

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

2. Midpoint Formula :-

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

3. Section Formula :-

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

4. Area of triangle :-

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

5. Centroid of a triangle :-

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