If the points A(3,4),B(x₁,y₁) and c(x₂,y₂) are such that both 3,x₁,x₂ and 4,y₁,y₂ are in A.P., then

Correct Answer is : A. B, C are collinear points

A, B. C are vertices of an isosceles triangle

A, B, C arc vertices of a right angled triangle

A, B, C are vertices of a scalene triangle

A, B, C are vertices of an equilateral triangle

Correct Answer is : A. B, C are collinear points

Test Index

KEAM 2015 Math Paper

Question : 73 of 120

Marks: +1, -0

If the points

A(3,4),B(x_1,y_1)

c(x_2,y_2)

3,x_1,x_2

4,y_1,y_2

are in A.P., then

Solution:

Given points are

A(3,4), B(x_{1}, y_{1})

and

C(x_{2}, y_{2})

since,

3, x_{1}, x_{2}

and

4, y_{1}, y_{2}

are in

A P

Then,

\\;\\; 2 x_{1}=3+x_{2}

and

2 y_{1}=4+y_{2}

\Rightarrow \\;\\; x_{1}=\\;\frac{3+x_{2}}{2}

and

y_{1}=\\;\frac{4+y_{2}}{2}

This shows that

B

is the mid-point of the line segment joining

A

and

C .

Hence,

A, B

and

C

are collinear.

Go to Question:

Prev Question

Next Question