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Coordinate Geometry basic concepts

CAT Coordinate Geometry is an important topic for preparations. Coordinate Geometry is the most interesting concepts of mathematics. This is a link between geometry and algebra in CAT exams. Aspirants should expect a few questions from coordinate Geometry. As quantitative section contain a total of 34 questions and out of that few questions are from coordinate Geometry. A coordinate Geometry is the most graphs and coordinates based questions.

Clearing your coordinate geometry concepts will enhance your accuracy level in exams. Which are are explained along with its formulas and their derivations. Hence, Pay attention to concepts and formulas. As you all know coordinate geometry topics contain good weightage in the CAT exam. Hence this become an important topic for exams.

In this article, we learn about some of the important dimensions of CAT coordinate geometry. All important aspects related to the topic will be covered. The aspirant would understand how to approach questions when his concepts become clear. In addition, one could easily ace coordinate geometry just by formulas and basic concepts clarity.

Also read: How to Prepare for CAT

MATHEMATICS: FORM ONE: Topic 10 - COORDINATE GEOMETRY - MSOMI BORA

Introduction to Coordinate Geometry for CAT exams.

Coordinate geometry (or analytic geometry) is the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc. There are certain terms in Cartesian geometry. That should be clear properly . Hence, the terms include are as follow:

Coordinate Geometry Terms
Coordinate Geometry Definition It is one of the branches of geometry. Where the position of a point is defined using coordinates.
What do you understand by the term Coordinates? Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
What do you understand by the term Coordinate Plane? A coordinate plane is a 2D plane. Which is formed by the intersection of two perpendicular lines. Line denotes as the x-axis and y-axis.
Give Distance Formula The distance between two points situated in A(x1,y1) and B(x2,y2)
Give Section Formula Section formula is to divide any line into two parts, in m:n ratio
Define Mid-Point Theorem Mid-Point Theorem is to find the coordinates. At which a line is divided into

Important Formula's of Coordinate Geometry for CAT exams.

Now, Let us have a look at some formulas for coordinate geometry. So we will use the below picture as a reference for the formulas.

Coordinate Geometry

Formula's that aspirants should kept in mind

  • Slope of PQ = m =
  • Equation of PQ is as below:

or y = mx + c

  • The product of the slopes of two perpendicular lines is –1.
  • The slopes of two parallel lines are always equal. If m1 and m2 are slopes of two parallel lines, then m1=m2.
  • The distance between the points (x1, y1) and (x2, y2) is
  • If point P(x, y) divides the segment AB, where A (x1, y1) and B (x2, y2), internally in the ratio m: n, then,
    x= (mx2 + nx1)/(m+n) and y= (my2 + ny1)/(m+n)
  • If P is the midpoint then,

  • If G (x, y) is the centroid of triangle ABC, A (x1, y1), B (x2, y2), C (x3, y3), then,
    x = (x1 + x2 + x3)/3 and y = (y1 + y2 + y3)/3
  • If I (x, y) is the in-center of triangle ABC, A (x1, y1), B (x2, y2), C (x3, y3), then,

where a, b and c are the lengths of the BC, AC and AB respectively.

  • The equation of a straight line is y = mx + c, where m is the slope and c is the y-intercept (tan = m, where is the angle that the line makes with the positive X-axis).
  • If two intersecting lines have slopes m1 and m2 then the angle between two lines θ will be tan θ = (m1−m2) / (1+m1m2)
  • The length of perpendicular from a point (x1 ,y1 ) on the line AX+BY+C = 0 is

Then P = (Ax1+By1+C) / (A2+B2)

Equations of a lines:

If you want to understand the concept of equation for clarity let look below points.

1.General equation of a line A x + By = C

2.Slope intercept form y = mx + c (c is y intercept)

3. Point-slope form y – y1 = m (x – x1 ) (m is the slope of the line)

4.Intercept form x / a + y / b = 1 (where a and b are x and y intercepts respectively)

5.Two point form: (y−y1) / (y2−y1) = (x−x1) / (x2−x1)

Knowledge of Quadrants:

So we will use the below picture as a reference for understanding of the concept of equation for clarity let look below points.

1.Quadrant I => X is Positive Y is Positive

2.Quadrant II => X is Negative Y is Positive

3.Quadrant III => X is Negative Y is Negative

4.Quadrant IV => X is Positive Y is Negative

Area of a Triangle in Cartesian Plane of Coordinate Geometry

The area of a triangle In coordinate geometry whose vertices are (x1, y1), (x2, y2) and (x3, y3) . Then the area of triangle is calculated with this formula.

1/2|x1(y2 − y3) + x2(y3 – y1) + x3(y1 – y2)|

If the area of a triangle whose vertices are (x1, y1),(x2, y2) and (x3, y3) is zero, then the three points are collinear.

Coordinate Geometry Section Formula: To Find a Point Which Divides a Line into m:n Ratio

Consider a line A and B having coordinates (x1, y1) and (x2, y2), respectively. Let P be a point that which divides the line in the ratio m:n, then the coordinates of the coordinates of the point P is given as-

  • When the ratio m:n is internal: (mx2+nx1m+n,my2+ny1m+n)
  • When the ratio m:n is external: (mx2–nx1m–n,my2–ny1m–n)

So aspirants can follow the concepts and clear the concepts with clarity.

Coordinate Geometry Distance Formula: To Calculate Distance Between Two Points

Let the two points be A and B, having coordinates to be (x1, y1) and (x2, y2), respectively.

Thus, the distance between two points is given as- d=(x2−x1)2+(y2–y1)2

Distance Between two Points in Cartesian Plane

Examples Based On Coordinate Geometry Concepts

For Examples 1: Find the distance between points M (4,5) and N (-3,8).

Solution: Applying the distance formula we have,

d=(−3–4)2+(8–5)2
d=(−7)2+(3)2=49+9
then, d=58

For Example 2: Find the equation of a line parallel to 3x+4y = 5 and passing through points (1,1).

Solution: For a line parallel to the given line, the slope will be of the same magnitude.

Thus the equation of a line will be represented as 3x+4y=k

Substituting the given points in this new equation, we have

k = 3 × 1 + 4 × 1 = 3 + 4 = 7

Therefore the equation is 3x + 4y = 7

Coordinate Geometry Questions For Practice

  1. Calculate the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2, – 2) and B(3, 7).
  2. Find the area of the triangle having vertices at A, B, and C which are at points (2, 3), (–1, 0), and (2, – 4), respectively. Also, mention the type of triangle.
  3. A point A is equidistant from B(3, 8) and C(-10, x). Find the value for x and the distance BC

For CAT Quantitative section’s full guidance visit this link- https://catking.in/best-guide-for-preparation-of-cat-quantitative-ability/


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