Question

Prove that the points (1,4), (3, -2) and (-3, 16) are collinear.​

Answer 1

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★ Given that,

• A(1, 4)
• B(3, -2)
• C(-3, 16)

★ Collinear :

The points which lie on the same line is known as " Collinear points " .

★ Let,

• x1 = 1 ; y1 = 4
• x2 = 3 ; y2 = - 2
• x3 = - 3 ; y3 = 16

By using Area of triangle formula

$\frac{1}{2} | x_{1}(y _{2} - y _{3}) + x _{2}(y _{3} - y _{2}) + x_{3}(y _{1} - y _{2}) |$

Substitute the values.

$⟹ \frac{1}{2} | 1( - 2 - 16) + 3(16 - 4) + ( - 3)(4 - ( - 2)) |$

$⟹ \frac{1}{2} | 1( - 18) + 3(12) - 3(6)|$

$⟹ \frac{1}{2} | - 18 + 36 - 18|$

$⟹ \frac{1}{2} | - 36 + 36|$

$⟹ \frac{1}{2} |0|$

$⟹0$

∴ Hence, these points are collinear points.

Step-by-step explanation:

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