Answer

Verified

436.5k+ views

Hint:- Find slope of each line and check for collinearity.

As, three vertices of the triangle are given,

$ \Rightarrow $Let, ${\text{A}}\left( {0,\dfrac{8}{3}} \right),{\text{ }}B\left( {1,3} \right){\text{ }}$and $C\left( {82,30} \right)$be the vertices of a triangle.

And the triangle will be $\Delta {\text{ABC}}$

Let, ${m_1}$be the slope of side AB.

$ \Rightarrow $So, ${m_1} = \left( {\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}} \right){\text{ }}$where $({x_1},{y_1})$ and $({x_2},{y_2})$ are the points A and B.

$ \Rightarrow $So, ${m_1} = \left( {\dfrac{{3 - \dfrac{8}{3}}}{{1 - 0}}} \right) = \dfrac{1}{3}$

Let, ${m_2}$ be the slope of side BC.

$ \Rightarrow $So, ${m_2} = \left( {\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}} \right)$ where $({x_1},{y_1})$ and $({x_2},{y_2})$ are the points B and C.

$ \Rightarrow $So, ${m_2} = \left( {\dfrac{{30 - 3}}{{82 - 1}}} \right) = \dfrac{{27}}{{81}} = \dfrac{1}{3}$

$ \Rightarrow $ As we have proved above that, ${m_1} = {m_2} = \dfrac{1}{3}$

And we know that if slopes of two lines are same and passes through same point (here B)

Then the lines are collinear.

So, therefore A, B and C are not the vertices of any triangle.

Because A, B and C lie on the same line. Hence, they are collinear.

Hence, the correct option will be D.

Note:- In such type of questions the easiest and efficient way to find the type of triangle

is by finding the slope of each line. So, first we had to find the slope of each line then we can

also find the length of each side by using distance formula and then we will easily get which type

triangle is given.

As, three vertices of the triangle are given,

$ \Rightarrow $Let, ${\text{A}}\left( {0,\dfrac{8}{3}} \right),{\text{ }}B\left( {1,3} \right){\text{ }}$and $C\left( {82,30} \right)$be the vertices of a triangle.

And the triangle will be $\Delta {\text{ABC}}$

Let, ${m_1}$be the slope of side AB.

$ \Rightarrow $So, ${m_1} = \left( {\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}} \right){\text{ }}$where $({x_1},{y_1})$ and $({x_2},{y_2})$ are the points A and B.

$ \Rightarrow $So, ${m_1} = \left( {\dfrac{{3 - \dfrac{8}{3}}}{{1 - 0}}} \right) = \dfrac{1}{3}$

Let, ${m_2}$ be the slope of side BC.

$ \Rightarrow $So, ${m_2} = \left( {\dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}} \right)$ where $({x_1},{y_1})$ and $({x_2},{y_2})$ are the points B and C.

$ \Rightarrow $So, ${m_2} = \left( {\dfrac{{30 - 3}}{{82 - 1}}} \right) = \dfrac{{27}}{{81}} = \dfrac{1}{3}$

$ \Rightarrow $ As we have proved above that, ${m_1} = {m_2} = \dfrac{1}{3}$

And we know that if slopes of two lines are same and passes through same point (here B)

Then the lines are collinear.

So, therefore A, B and C are not the vertices of any triangle.

Because A, B and C lie on the same line. Hence, they are collinear.

Hence, the correct option will be D.

Note:- In such type of questions the easiest and efficient way to find the type of triangle

is by finding the slope of each line. So, first we had to find the slope of each line then we can

also find the length of each side by using distance formula and then we will easily get which type

triangle is given.

Recently Updated Pages

Assertion The resistivity of a semiconductor increases class 13 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

Trending doubts

What type of defect is shown by NaCl in a Stoichiometric class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Distinguish between tetrahedral voids and octahedral class 12 chemistry CBSE

Derive an expression for electric potential at point class 12 physics CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE