Q22 of 52 Page 1

Find the value of p, if the points A(1, 2), B(3, p) and C(5, - 4) are collinear.

Given,


Points A (1, 2), B (3, p) and C (5, - 4) are collinear


Area of the triangle = 0


As,


Area of the triangle = 1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)] = 0


∴ 1[p – (- 4)]+3[- 4 – 2] + 5[2 – p] = 0


P+4 – 18 + 10 – 5p = 0


- 4 – 4p = 0


- 4p = 4


P = 4/-4 = - 1


Therefore p = -1


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