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Let points A,B and C lie on lines y-x=0,...

Let points A,B and C lie on lines y-x=0, 2x-y=0 and y-3x=0, respectively. Also, AB passes through fixed point P(1,0) and BC passes through fixed point Q(0,-1). Then prove that AC also passes through a fixed point and find that point.

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To solve the problem step by step, we will follow the given conditions and derive the required fixed point through which line AC passes. ### Step 1: Identify Points on Given Lines Let: - Point A lies on the line \( y - x = 0 \) (i.e., \( y = x \)). So, we can represent point A as \( A(\alpha, \alpha) \). - Point B lies on the line \( 2x - y = 0 \) (i.e., \( y = 2x \)). So, we can represent point B as \( B(\beta, 2\beta) \). - Point C lies on the line \( y - 3x = 0 \) (i.e., \( y = 3x \)). So, we can represent point C as \( C(\gamma, 3\gamma) \). ...
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