Home
Class 12
MATHS
Consider the triangle whose vetices are ...

Consider the triangle whose vetices are (0,0) , (5,12) and (16,12).

Text Solution

Verified by Experts

The correct Answer is:
a to s;b to p;c to q;d to s
(a). Centroid is `((0+5+16)/(3),(0+12+12)/(3))-=(7,8)`
(b). Let the coordinates of circumcenter be `O(x,y)` therefore,
`OA=OB=OC`
` therefore x^2+y^2=(x-5)^2+(y-12)^2=(x-16)^2+(y-12)^2`
` therefore x^2+y^2=(x-5)^2+(y-12)^2`
or `10x+24y=169`
and `(x-5)^2+(y-12)^2=(x-16)^2+(y-12)^2`
or `2x=21`
Solving, we get
`x=(21)/(2),y=(8)/(3)`
(c). `I-=((0xx11+5xx20+16xx13)/(13+20+11),(0xx11+12xx20+13xx12)/(13+20+11))-=(7,9)`
(d). `I_2-=((-5xx20+13xx16+11xx0)/(-20+13+11),(-12xx20+0xx11+13xx12)/(-20+13+11))-=(27,-21)`.
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Numerical value|12 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise JEE Main|6 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Linked|10 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Find the circumcentre and circumradius of the triangle whose vertices are (3,4) , (3,-6) and (-1,2).

Orthocentre of the triangle whose vertices are (0,0) (3,4) and (4,0) is-

The distance between the circumcenter and the orthocentre of the triangle whose vertices are (0,0),(6,8), and (-4,3) is Ldot Then the value of 2/(sqrt(5))L is_________

The distance between the circumcentre and orthocentre of the triangle whose vertices are (0,0),(6,8)and (-4,3) is

Find the orthocentre of the triangle whose vertices are (0,0),(3,0), and (0,4)dot

Number of points with integral co-ordinates that lie inside a triangle whose co-ordinates are (0, 0), (0, 21) and (21,0).

By vector method find the area of the triangle whose vertices are (1,1,1) ,(2,0,1) and (3,-2,0)

The incentre of the triangle whose vertices are (-36, 7), (20, 7) and (0, -8) is :

Calculate the direction cosines of the sides of the triangle whose vertices are A(4, 5, 0), B(2, 6, 2) and C(2, 3, -1).