If the three points (3q, 0), (0, 3p), and (1, | vedclass

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(C) Let the points be $A(3q, 0)$, $B(0, 3p)$, and $C(1, 1)$.Since the points are collinear, the slope of $AC$ must be equal to the slope of $BC$.Slope

Vedclass · Accepted Answer

$\frac{1}{p} + \frac{1}{q} = 3$

Vedclass · Answer

(C) Let the points be $A(3q, 0)$, $B(0, 3p)$, and $C(1, 1)$.Since the points are collinear, the slope of $AC$ must be equal to the slope of $BC$.Slope of $AC = \frac{1 - 0}{1 - 3q} = \frac{1}{1 - 3q}$.Slope of $BC = \frac{3p - 1}{0 - 1} = \frac{3p - 1}{-1} = 1 - 3p$.Equating the slopes: $\frac{1}{1 - 3q} = 1 - 3p$.$1 = (1 - 3p)(1 - 3q)$.$1 = 1 - 3q - 3p + 9pq$.$3p + 3q = 9pq$.Dividing both sides by $3pq$, we get $\frac{3p}{3pq} + \frac{3q}{3pq} = \frac{9pq}{3pq}$.$\frac{1}{q} + \frac{1}{p} = 3$.

If the three points $(3q, 0)$, $(0, 3p)$, and $(1, 1)$ are collinear, then which one is true?

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