#### CHAPTER AT A GLANCE

**1. Coordinate of a Point in XY- Plane**

The perpendicular distance of x a point from they-axis is called its x-coordinate or abscissa. The perpendicular distance y of a point from the x-axis is called its y-coordinate or ordinate. The x and y taken together in order is called coordinate of a point denoted by (x, y). The coordinate of the points on x-axis are of the form (x, 0) and the points on they-axis are of the form (0,y). Coordinate of origin is (0, 0).

**2. Sign-conventions in the XV-Plane**

The x and y-axis divide the plane into four parts known as quadrants denoted by I, II, III and IV. The sign of x-and y-coordinate in each of the quadrant is shown below:

**3. Distance Formula**

The distance between any two points

P(x1, y1) and Q(x2, y2) in the plane is given by,

Also the distance of the point P(x1, y1) from the origin is

**4. Section Formula**

The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) internally in the ratio m1: m2

(ii) The coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2) externally in the ratio, m1 : m2

(iii) If the ratio in which P divides AB is K : I, then the coordinates of the point P will be

**5. Mid-point Formula**

The coordinates of the mid point P of the line segment joining the points A(x1, y1) and B(x2, y2) is

**6. Area of a Triangle**

The area of MBC formed by the vertices A(x1,y1), B(x2, y2) and C(x3,y3) is given by

**Note:**

(i) Area of triangle= 1/2 x base x Altitude

(ii) Area of polygon can be calculated by dividing it into the triangular region.

(iii) If three points are collinear then area of the triangle formed by them is

zero.

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