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| 1. |
Prove that the points (a,0),(0,b,(1,1)are collinear if 1/a+1/b=1 |
| Answer» Since (a, 0), (0, b) and (1, 1) are collinearArea = 0{tex}\\frac{1}{2}\\left[ {{x_1}({y_2} - {y_3}) + {x_2}({y_3} - {y_1}) + {x_3}({y_1} - {y_2})} \\right] = 0{/tex}{tex} \\Rightarrow \\frac{1}{2}\\left[ {a(b - 1) + 0(1 - 0) +1 (0 - b)} \\right] = 0{/tex}{tex} \\Rightarrow {/tex}\xa0ab - a - b = 0{tex} \\Rightarrow {/tex}\xa0ab = a + bDividing by ab,{tex}\\frac{{ab}}{{ab}} = \\frac{a}{{ab}} + \\frac{b}{{ab}}{/tex}{tex}\\frac{1}{a} + \\frac{1}{b} = 1{/tex} | |