Important Formulas: Coordinate Geometry

## Coordinate Geometry

• Coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

### Coordinate Geometry Formulas and Basic Concept

• The point of intersection of the x and the y-axis is known as the origin. At this point, both x and y are 0.
• The values on the right-hand side of the x-axis are positive and the values on the left-hand side of the x-axis are negative.
• Similarly, on the y-axis, the values located above the origin are positive and the values located below the origin are negative.

### Formulas for Coordinate Geometry Questions

• Distance between two points A(x1, y1) and B(x2, y2)
• Slope of line when two points are given (x1, y1) and (x2, y2)
• Slope of line when linear equation is given
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x1, y1) and B(x2, y2) internally in the ratio m:n is given by
• The co-ordinates of a point R(x,y) that divides a line segment joining two points A(x1, y1) and B(x2, y2) externally in the ratio m:n is given by
• Centroid of a triangle with its vertices (x1, y1), (x2, y2), (x3,y3)
• Area of a Triangle with its vertices A(x1, y1), B(x2, y2), C(x3,y3)
• Division of a line segment by a point

If a point p(x, y) divides the join of A(x1, y1) and B(x2, y2), in the ratio m: n, then

• The equation of a line in slope intercept form is Y= mx+ c, where m is its slope.

The equation of a line which has gradient m and which passes through the point (x1, y1) is =

y – y1 = m(x – x1).

Example: If the slope of a line is -2/3 and it passes through the point (2, 5), find the equation of the line in point-slope form.
Equation of the line passing through points P(3, 8) and Q(5, -2):

Using the point-slope form: y – y1 = m(x – x1)
y – 8 = -5(x – 3)
y – 8 = -5x + 15
y = -5x + 23

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