Tips to learn Coordinate Geometry : CAT Quantitative Aptitude

Cartesian Plane

• The Cartesian plane is divided into four quadrants by the two axes, the x-axis and the y-axis.

• A point in the Cartesian plane has an x and a y coordinate, which determine its position completely.

• Let two points be P(x1, y1) and Q(x2, y2), then

           Distance, PQ =

• Midpoint, M =

      R divides PQ internally in the ratio l : m, then

• R divides PQ externally in the ratio l : m, l > m, then

• Angles are measured in an anti-clockwise direction with the positive x-axis at 0°.

Lines

• The gradient or slope of a line is the change in y per unit change in x, denoted by m.

• m = tanø, whereø is the angle that a line makes with the positive x-axis.

• Given two points P(x₁, y₂) and Q(x₂, y₂), the gradient of the line through P and Q is m =

More about Straight Lines

• The equation of a straight line can be written in many forms. (x1, y1) and (x2, y2) are two points on the line, m denotes the slope and c the y-intercept.

• Point-Slope Form: (y – y₁) = m(x – x₁)

• Two-Point Form:  

• Slope-Intercept Form: y = mx + c
• Axes-Intercept Form:   for a line passing through (a, 0) and (0, b)

• Symmetric Form: , where tanΘ = m

• General Equation: ax + by + c = 0, at least one of a, b not equal to 0.

• Two lines are parallel if their gradients are equal.

• Two lines are perpendicular if the product of their gradients is -1.

• The angle e between two lines in given by

     tanΘ = where m₁, m₂ are the gradients of the two lines.

• Distance of point (x₁, y₁) from the line ax + by + c = 0 is