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Question

If the points A(x, y), B(−5, 7) and C(−4, 5) are collinear, then show that 2x + y + 3 = 0.

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Solution

The given points are A(x, y), B(−5, 7) and C(−4, 5).
So, (x1 = x, y1 = y), (x2 = −5, y2 = 7) and (x3 = −4, y3 = 5).
If the given points are collinear, then:
x1y2-y3+x2y3-y1+x3y1-y2 =0x7-5+-55-y+-4y-7=0x2-55-y-4y-7=02x-25+5y-4y+28=02x+y+3 = 0

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