Home
Class 12
MATHS
If (1,4) is the centroid of a triangl...

If `(1,4)` is the centroid of a triangle and the coordinates of its any two vertices are `(4,-8)` and `(-9,7),` find the area of the triangle.

Text Solution

Verified by Experts

The correct Answer is:
`166.5` sq.unit
Let the given triangle be ABC.
centroid is `G(1,3)` and two vertices of triangle are `B(4,-8)` and `C(-9,7)`
`"Area of triangle GBC"=(1)/(2)||{:(1,,4),(4,,-8),(-9,,7),(1,,4):}||`
`=(1)/(2)|[-8-16+28-72-36-7]|`
`=555` sq.units.
Hence, area of triangle `ABC=3xx55.5=166.5`sq.units
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.4|8 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.5|5 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.2|8 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

If the centroide of a triangle is at (4,-2) and two of its vertices are (3,-2) and ( 5,2) then find the thrid vertex of the triangle .

If the centroid of a triangle is at (4,-2) and two of its vertices are (3,-2) an (5,2) then find the third vertex of the triangle .

The centroid of a triangle is (2,7) and two of its vertices are (4, 8) and (-2, 6). The third vertex is

If the centroid of a triangle is at (1,3) and two of its vertices are (7,-6) and (8,5) then the third is.....

If the centroid of a triangle is at (10,-1) and two vertices are (3,2) and (5,-11). Find the third vertex of a triangle .

Consider the triangle whose vertices are (-1,0),(5,-2) and (8,2). Find the centroid of the triangle.

Consider the triangle whose vertices are (0,6) , (8,12) and (8,0). Find the centroid of the triangle.

Find the area of the triangle whose vertices are (3,8) ,(-4,2) and ( 5,1 )

Find the centroid of the triangle whose vertices are (2,-5),(5,11) and (9,9).