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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.
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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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