# Tips And Tricks And Shortcuts on Coordinate Geometry

## Tips And Tricks and Shortcuts On Coordinate geometry

Coordinate Geometry  is also known as  system of geometry where the position of points on the plane is described using some ordered pair of numbers

### Tips and Tricks and Shortcuts for Coordinate Geometry Problem’s.

• Here, are Coordinate Geometry tips and tricks and shortcuts. Co-ordinate Geometry are most asked in recruitment exams. Learn, the tricks on Coordinate Geometry easily, and efficiently.
• Here are the types of problems given for solving the coordinate geometry questions based on areas , length of segment and distance time graphs

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

Question 1. Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0

Options:

A. 2x – 3y + 5 = 0

B. 2x + 3y + 5 = 0

C. 2x – 3y – 5 = 0

D. 2x + 3y – 5 = 0

Solution :    x1 = 2; y1 = 3

The given line is 3x + 2y + 4 = 0

Line perpendicular to it will have slope m = $\frac{2}{3}$

Thus equation of line through (2, 3) and slope $\frac{2}{3}$ = y – y1 = m(x – x1)

(y – 3) = $\frac{2}{3}$ (x – 2)

y – 3 = 2x –$\frac{4}{3}$

3y – 9 = 2x – 4

2x – 3y + 5 = 0

Correct option: A

### Type 2: Coordinate Geometry Tips and Tricks and Shortcuts. In which quadrant does the point lie?

Question 1. In which quadrant does the point (-2, 3) lie?

Options:

Solution:    The point is negative in the x axis and positive for the y axis, thus the point must lie in the 2nd quadrant.

Correct option: 2

### Type 3: Tips and Tricks for Coordinate Geometry.Find length of the segment or coordinates

Question 1. 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?

Options:

A. 2, 1

B. 2, 5

C.  $\frac{12}{5}$, $\frac{19}{5}$

D.  12, $\frac{15}{19}$

Solution:    We know that, x= $\frac{ m x_{2} + nx_{1}}{m + n}$ and y= $\frac{my_{2} + ny_{1} }{m + n}$

x = 2 × 3 + 3 × $\frac{2}{2}$+ 3

x = $\frac{12}{5}$

y = 2 × 5 + 3 × $\frac{3}{2}$ + 3

y = $\frac{19}{5}$

Therefore, (x, y) = $\frac{12}{5}$, $\frac{19}{5}$

Correct option: 3

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

Question 1. Find the area of the triangle formed by the vertices (1, 2), (3,5) and (-2, 3)

Options:

A. 2.5

B. 3.5

C. 5.5

D. 6

Solution :    Area of triangle = A = $\frac{1}{2} ×[ (x_{1}(y_{2}-y_{3}) + (x_{2}(y_{3}-y_{1}) ) + (x_{3}(y_{1}-y_{2}) )]$

A =$\frac{1}{2} ×[ (1(5-3) + (3(3-2) ) + (2(2-5) )]$

A =$\frac{1}{2} ×[ (1(2) + (3(1) ) + (2(-3) )]$

A = $\frac{1}{2} ×[ 2 + 3 + 6]$

A = $\frac{1}{2} ×[11]$

A = 5.5

Correct option: C