Home
Class 12
MATHS
A B C is an isosceles triangle. If the c...

`A B C` is an isosceles triangle. If the coordinates of the base are `B(1,3)` and `C(-2,7)` , the coordinates of vertex `A` can be (a)`(1,6)` (b) `(-1/2,5)` (c)`(5/6,6)` (d) none of these

A

(1,6)

B

`(-1//2,5) `

C

`(-5//6,6) `

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let the vetex of triangle be `A(x,y)`.
Then the vetex `A(x,y)` is equidistant from B and C because ABC is an isosceles triangle. Therefore,
`(x-1)^2+(y-3)^2=(x+2)^2+(y-7)^2`
or `6x-8y+43=0`
Thus, any point lying on this line can be the vertex A is `(5//6,6)`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Comprehension)|10 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

The value of tan[cos^(-1)(4/5)+tan^(-1)(2/3)] is 6/(17) (b) 7/(16) (c) (16)/7 (d) none of these

In an isosceles triangle ABC, the coordinates of the points B and C on the base BC are respectively (1, 2) and (2. 1). If the equation of the line AB is y= 2x, then the equation of the line AC is

If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre lies at the origin, and the centroid on the line x+y=7 , then the third vertex lies at (a) (7,4) (b) (8,14) (c) (12 ,21) (d) none of these

The centroid of a triangle ABC is at the point (1,1,1) . If the coordinates of A and B are (3,-5,7) and (-1,7,-6) , respectively, find the coordinates of the point C.

The area of triangle A B C is 20c m^2dot The coordinates of vertex A are -5,0) and those of B are (3,0)dot The vertex C lies on the line x-y=2 . The coordinates of C are (5,3) (b) (-3,-5) (-5,-7) (d) (7,5)

In A B C , the coordinates of B are (0,0),A B=2,/_A B C=pi/3, and the middle point of B C has coordinates (2,0)dot The centroid o the triangle is (a) (1/2,(sqrt(3))/2) (b) (5/3,1/(sqrt(3))) (c) (4+(sqrt(3))/3,1/3) (d) none of these

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0) , B (4, 5) and C(6, 3).

Find the area of the triangle formed by the points A(0, – 1), B(– 2, 6) and C(– 3, – 5)

The vertices of Delta ABC are A(7,2,1),B(6,0,3) and C(4,2,4). Find angleABC .

A triangle A B C with vertices A(-1,0),B(-2,3/4), and C(-3,-7/6) has its orthocentre at Hdot Then, the orthocentre of triangle B C H will be (-3,-2) (b) 1,3) (-1,2) (d) none of these

Home
Profile