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Question
Find the value of y, if the points A(3, 4), B(6, y) and C(7, 8) are collinear.
Solution
Given points A(3, 4), B(6, y) and C(7, 8) are collinear.
The area of the triangle produced by the points is zero since they are collinear.
∴ `1/2 |x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2)|` = 0
`1/2 |3(y - 8) + 6(8 - 4) + 7(4 - y)|` = 0
3y – 24 + 48 – 24 + 28 – 7y = 0
28 – 4y = 0
4y = 28
y = 7
Hence, the value of y is 7.
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