Question

Find area of the triangle formed by sides x+4y-9=0, 9x+10y+23=0, 7x+2y-11=0​

Answer 1

Given : sides

x+4y-9=0,

9x+10y+23=0,

7x+2y-11=0

To Find :  area of the triangle formed by sides

Solution:

x+4y-9=0

9x+10y+23=0

7x+2y-11=0

x+4y-9=0  and 9x+10y+23=0

=> x = - 7 , y = 4

x+4y-9=0  and  7x+2y-11=0

=> x = 1 , y = 2

9x+10y+23=0 and  7x+2y-11=0

=> x = 3 , y = - 5

Vertex are

(-7 , 4) , ( 1 , 2) , ( 3 , - 5)

Area = (1/2) | -7 (2 - (-5) + 1 ( -5 - 4)  + 3(4 - 2) |

= (1/2) | -49 - 9 + 6 |

= (1/2) | - 52|

= (1/2) 52

= 26

area of the triangle formed by sides  = 26 Sq units

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