Quants Menu
- HCF and LCM
- Number System
- Number Decimals & Fractions
- Surds and Indices
- Divisibility
- Ages
- LCM
- HCF
- Inverse
- Speed Time and Distance
- Work and Time
- Boats and Streams
- Pipes and Cisterns
- Averages
- Allegations and Mixtures
- Ratio and Proportions
- Simple & Compound Interest
- Simple Interest
- Compound Interest
- Percentages
- Profit & Loss
- Successive Discount 1
- Successive Discount 2
- AP GP HP
- Arithmetic Progressions
- Geometric Progressions
- Harmonic Progressions
- Probability
- Permutation & Combination
- Combination
- Circular Permutation
- Geometry
- Heights and Distances
- Perimeter Area and Volume
- Coordinate Geometry
- Venn Diagrams
- Set Theory
- Algebra
- Linear Equations
- Quadratic Equations
- Logarithms
- Clocks
- Calendars
- Clocks and Calendars
- Finding remainder of large powers
PREPINSTA PRIME
How To Solve Coordinate Geometry Quickly
Ways to solve Coordinate Geometry Problems Quickly
Solve Coordinate Geometry Questions Quickly
- A 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.
How To Solve Coordinate Geometry Questions Quickly:
Type 1: How To Solve Quickly Coordinate Geometry -Distance and Equation of Straight Line
Question 1: Find the distance between points A(–2,-5) and B(6,1)?
Options:
A. 100
B. 10
C. 20
D. 5
Solution: AB = \sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2}
AB =\sqrt{(6- (-2))^2 + (1- (-5))^2}
AB = \sqrt{(6+2)^2 + (1+5)^2}
AB = \sqrt{(8)^2 + (6)^2}
AB = \sqrt{64 + 36}
AB =\sqrt{100}
AB = 10
Correct option: B
Question 2: Find the equation of line whose end points are (4, 5) and (2, 8).
Options:
A. 3x – 2y -2 = 0
B. 3x + 2y -2 = 0
C. 3x + 2y + 2 = 0
D. 3x – 2y + 2 = 0
Solution: We know that,
y – y1 = m(x – x1)
m = \frac{(y_{1}- y_{2})}{(x_{1}- x_{2}}
Therefore, y – y1 = \frac{(y_{1}- y_{2})}{(x_{1}- x_{2})} × (x – x1)
y – 5 = \frac{(8- 5)}{(4 – 2)} × x – 4
y – 5 =\frac{3}{2} ×( x – 4)
2y – 10 = 3x – 12
3x – 2y -2 = 0
Correct option: A
Question 3: Two points (a + 3, b + k) and (a, b) are on the line x – 2y + 9 = 0. Find the value of k.
Options:
A. \frac{1}{2}
B. \frac{2}{3}
C.\frac{3}{4}
D.\frac{3}{2}
Solution: x – 2y + 9 = 0
y = \frac{x}{2}+ \frac{9}{2}
Slope of the line = \frac{1}{2}
Slope of the line using two points = b + k – \frac{b}{a} + 3 –a
= \frac{k}{3}
\frac{k}{3} = \frac{1}{2}
k = \frac{3}{2}
Correct option: D
Type 2: How To Solve Coordinate Geometry Quickly. In which quadrant does the point lie?
Question 1: In which quadrant does the point (-7, 3) lie?
Options:
A. I quadrant
B. II quadrant
C. III quadrant
D. IV quadrant
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: B
Question 2: In which quadrant does the point (2, 3) lie?
Options:
A. I quadrant
B. II quadrant
C. III quadrant
D. IV quadrant
Solution: Both points are positive. Therefore they will lie in 1st quadrant
Correct option: A
Question 3: In which quadrant does the point (-10, -3) lie?
Options:
A. I quadrant
B. II quadrant
C. III quadrant
D. IV quadrant
Solution: Both points are negative. Therefore they will lie in 3th quadrant.
Correct option: C
Type 3: Solve Quickly Coordinate Geometry Questions.
Find the Coordinates
Question 1: Find the co-ordinates of the centroid of a triangle whose vertices are (0, 4), (6, 10) and (9, 4).
Options:
A. 6, 5
B. 7, 5
C. 5, 6
D. 5, 7
Solution: We know that, Centroid of a triangle with its vertices (x1,y1), (x2 ,y2), (x3,y3)
C =\frac{x_{1}+ x_{2} + x_{3}}{3}, \frac{y_{1}+ y_{2} + y_{3}}{3}
C =\frac{0+ 6 + 9}{3}, \frac{4+ 10 + 4}{3}
C =\frac{15}{3}, \frac{18}{3}
C = 5, 6
Correct option: C
Question 2: If the distance between two points A(a, –3) and B(3, a) is 6 unit, then a = ?
Options:
A. ± 3
B. – 5
C. 4
D. 0
Solution: We know that, Distance between two points A(x1, y1) and B(x2, y2)
AB = \sqrt{(x_{2}- x_{1})^2 + (y_{2}- y_{1})^2}
AB = \sqrt{(3- a)^2 + (a+ 3)^2}
AB = √2a² + 18
According to question,
\sqrt{2}a²+18 = 6
2a² + 18 = 36
a² = 9
a = ±3
Correct option: A
Question 3: The line passing through (4,3) and (y,0) is parallel to the line passing through (–1,–2) and (3,0). Find the value of y?
Options:
A. 2
B. -2
C. -1
D. 1
Solution: Slope of line passing through (4,3) (y,0)
m = \frac{(y_{1}- y_{2})}{(x_{1}- x_{2})}
m_{1}= \frac{(3- 0)}{(4- y)}
Slope of line passing through (–1,–2) (3,0)
m_{2}= \frac{(-2 – 0)}{(-1- 3)}
If two lines are parallel then, there slopes are equal
m_{1}= m_{2}
\frac{3}{4- y } = \frac{-2}{-4}
\frac{3}{4- y } = \frac{2}{4}
8 – 2y = 12
– 2y = 12 – 8
– 2y = 4
y = \frac{4}{-2}
y = – 2
Correct option: B
Type 4: Coordinate Geometry Solve Questions Quickly.
Find the area
Question 1: A(a,b), B(c,d) and C(e,f) are the vertices of a triangle. Given that:
Option 1: AB + BC > AC
Option 2: Area of the triangle = \frac{1}{2} ×[ (a(c-e) + (c(f-b) ) + (e(b-d) )]
Which of the following are true?
Options:
A. Option I is true
B. Option II is true
C. Both are true
D. None of the above
Solution: The formula given in option II is wrong.
The correct formula is
A = \frac{1}{2} ×[ (a(d-f) + (c(f-b) ) + (e(b-d) )]
Correct option: A
Question 2: Find the area of the triangle formed by the vertices (31, 25), (23, 30) and (33, 28)
Options:
A. 25
B. 15
C. 19
D. 17
Solution: Area of triangle = \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} ×[ (31(30-28) + (23(28-25) ) + (33(25-30) )]
A = 17
Correct option: D
Question 3: Find the area of the triangle formed by the vertices (-8, 19), (-7, 31) and (13, 25)
Options:
A. 125
B. 135
C. 119
D. 123
Solution: Area of triangle = \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} ×[ (- 8 (31-25) + (7(25 – 19) ) + (13(19-31) )]
A = 123
Correct option: D
Prime Course Trailer
Related Banners
Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription
Also Check Out
Get over 200+ course One Subscription
Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others
- Geometry – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Heights and Distances – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Perimeter Area and Volume – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Venn Diagrams – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Set Theory – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Geometry – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Heights and Distances – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Perimeter Area and Volume – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Venn Diagrams – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Set Theory – Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts
Login/Signup to comment