Coordinate Geometry Tips and Tricks for Government Exams

Introduction 

Here are some tips, tricks, and shortcuts for Coordinate Geometry, a topic frequently featured in recruitment exams. Easily and efficiently learn these strategies for solving problems related to coordinate geometry, including areas, length of segments, and distance-time graphs. 

Type 1:  Coordinate Geometry Questions Tips and Tricks and Shortcuts for.

Q: Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0
(a) 2x – 3y + 5 = 0
(b) 2x + 3y + 5 = 0
(c) 2x – 3y – 5 = 0
(d) 2x + 3y – 5 = 0
Ans: (a)
x₁ = 2; y₁ = 3
The given line is 3x + 2y + 4 = 0
Line perpendicular to it will have slope m = 2/3
Thus equation of line through (2, 3) and slope 2/3 = y - y₁ = m(x - x₁)


3y – 9 = 2x – 4
2x – 3y + 5 = 0
3y – 9 = 2x – 4
2x – 3y + 5 = 0

Type 2: Tips Tricks and Shortcuts for In which quadrant does the point lie?

Q: In which quadrant does the point (-2, 3) lie?
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant
Ans: (b)
Solution:  The point is negative in the x axis and positive for the y axis, thus the point must lie in the 2nd quadrant.

Type 3: Tips and Tricks  for Find length of the segment or coordinates

Q: Find the coordinate of the point which will divide the line joining the point (2, 3) and (3, 5) internally in the ratio 2:3?
(a) 2, 1
(b) 2, 5
(c) 12/5, 19/5
(d) 12, 15/19
Ans: (c)
 We know that,


x = 12/5

y = 19/5
Therefore, (x, y) = 12/5, 19/5

Type 4: Tips Tricks and Shortcuts for Area of the Triangle in Coordinate Geometry 

Q: Find the area of the triangle formed by the vertices (1, 2), (3,5) and (-2, 3)
(a) 2.5
(b) 3.5
(c) 5.5
(d) 6
Ans: (c)
Area of triangle


A = 5.5