question_answer

A line L passes through the points (1,1) and (2, 0) and another line L' passes through \[\left( \frac{1}{2},0 \right)\] and perpendicular to L. Then, area of the triangle formed by the line L L' and y-axis is

A)  \[\frac{15}{8}\]                               

B)  \[\frac{25}{4}\]

C)  \[\frac{25}{8}\]                               

D)  \[\frac{25}{16}\]

Correct Answer: D

Solution :

 Idea Equation of line passing through two given points \[(x,y)\] and \[(x2,{{y}_{2}})\]is\[y-{{y}_{1}}=\frac{{{y}_{2}}-{{x}_{1}}}{{{y}_{2}}-{{y}_{1}}}(x-{{x}_{1}})\]Use this formula and find intersection point between two lines. To solve this question, we have to come the above method. Line L which passes through (1, 1) and (2, 0) is \[(y-1)=\frac{-1}{1}(x-1)\] \[y-1=-x+1\] \[x+y=2\]                            ..(i) Line L? is               \[(y-0)=1\left( x-\frac{1}{2} \right)\]                                 \[2y=2x-1\]                                 \[2y-2y=1\]                         ?(ii) On solving Eqs. (i) and (ii), \[x=\frac{5}{4},y=\frac{3}{4}\] Required area is \[=\frac{1}{2}.\] base x height \[=\frac{1}{2}\times \frac{5}{2}\times \frac{5}{4}=\frac{25}{16}\] TEST Edge The area of triangle between two curves' related questions are asked from this concept. To solve such types of questions, to understand basic definition of equation of line and also acquainted yourself with concept of graph transformation.