- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# State whether the following statements are true or false. Justify your answer.

The points $ (0,5),(0,-9) $ and $ (3,6) $ are collinear.

Given:

The points \( (0,5),(0,-9) \) and \( (3,6) \) are collinear.

To do:

We have to find whether the given statement is true or false.

Solution:

We know that,

If the points \( (0,5),(0,-9) \) and \( (3,6) \) are collinear, then the area of triangle is 0.

Area of a triangle $=\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]$

Therefore,

Area of the given triangle $=\frac{1}{2}[0(-9-6)+0(6-5)+3(5+9)]$

$=\frac{1}{2}[0+0+3(14)]$

$=3(7)$

$=21$

The area of the triangle formed by the given points is not equal to 0.

Therefore, points \( (0,5),(0,-9) \) and \( (3,6) \) are not collinear.

- Related Articles
- State whether the following statements are true or false. Justify your answer.The points $A (–1, –2), B (4, 3), C (2, 5)$ and $D (–3, 0)$ in that order form arectangle.
- State whether the following are true or false. Justify your answer.The value of tan \( A \) is always less than 1 .
- State whether the following statements are true or false. Justify your answer.The point \( \mathrm{A}(2,7) \) lies on the perpendicular bisector of line segment joining the points \( P(6,5) \) and \( Q(0,-4) \).
- State whether the following statements are true or false. Justify your answer.Points \( A(-6,10), B(-4,6) \) and \( C(3,-8) \) are collinear such that \( A B=\frac{2}{9} A C \).
- State whether the following statements are true or false. Justify your answer.The point P $(–2, 4)$ lies on a circle of radius 6 and centre $C (3, 5)$.
- State whether the following statements are true or false. Justify your answer.Point \( P(-4,2) \) lies on the line segment joining the points \( A(-4,6) \) and \( B(-4,-6) \).
- Write whether the following statements are true or false. Justify your answers.Every quadratic equation has exactly one root.
- State whether the following are true or false. Justify your answer.\( \cot A \) is the product of \( \cot \) and \( A \).
- Write whether the following statements are true or false. Justify your answers.Every quadratic equation has at least two roots.
- Write whether the following statements are true or false. Justify your answers.Every quadratic equations has at most two roots.
- Write whether the following statements are true or false. Justify your answers.Every quadratic equation has at least one real root.
- State whether the following are true or false. Justify your answer.\( \sin \theta=\frac{4}{3} \) for some angle \( \theta \).
- State whether the following statements are true or false. Justify your answer.Point \( P(5,-3) \) is one of the two points of trisection of the line segment joining the points \( A(7,-2) \) and \( B(1,-5) \).
- State whether the following are true or false. Justify your answer.\( \sec A=\frac{12}{5} \) for some value of angle \( A \).
- State whether the following are true or false. Justify your answer.\( \cos A \) is the abbreviation used for the cosecant of angle \( A . \)

Advertisements