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#### Question

If the points A(−1, −4), B(*b*, *c*) and C(5, −1) are collinear and 2*b* + *c* = 4, find the values of *b* and *c*.

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Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and (5k – 1, 5k) are collinear.

Find the area of the triangle whose vertices are:

(2, 3), (-1, 0), (2, -4)

In Fig. 8, the vertices of ΔABC are A(4, 6), B(1, 5) and C(7, 2). A line-segment DE is drawn to intersect the sides AB and AC at D and E respectively such that `(AD)/(AB)=(AE)/(AC)=1/3 `Calculate the area of ADE and compare it with area of ΔABC.

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If the points A(*x*, 2), B(−3, −4) and C(7, − 5) are collinear, then the value of *x* is:

(A) −63

(B) 63

(C) 60

(D) −60