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Find area of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)

Solution:
Your problem `->` area of a triangle whose vertices are A(4,1),B(-2,-3),C(6,7)


Here `A(4,1), B(-2,-3), C(6,7)` are the given points

`:. x_1=4, y_1=1, x_2=-2, y_2=-3, x_3=6, y_3=7`

Area of a triangle
`=1/2 |[x_1,y_1,1],[x_2,y_2,1],[x_2,y_2,1]|`

`=1/2 |[4,1,1],[-2,-3,1],[6,7,1]|`

`=1/2[4 xx (-3 × 1 - 1 × 7) -1 xx (-2 × 1 - 1 × 6) +1 xx (-2 × 7 - (-3) × 6)]`

`=1/2[4 xx (-3 -7) -1 xx (-2 -6) +1 xx (-14 +18)]`

`=1/2[4 xx (-10) -1 xx (-8) +1 xx (4)]`

`=1/2[-40 +8 +4]`

`=1/2[-28]`

`=-14`

`=14` (As area is positive)







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