Question

The line 2x + 3y = 12 meets the x-axis at A and
y-axis at B. The line through (5, 5) perpendicular to AB meets the x-axis, y-axis and the AB at C, D and E respectively. If O is the origin of coordinates, then the area of OCEB is :

• A. 23 sq. units
• B. 23/2 sq. units
• C. 23/3 sq. units
• D. None of these

Answer 1

Answer: (C)

23/3 sq. units

Answer 2

2x + 3y = 12 … (i)

x/6 + y/4 = 1 Ž A(6, 0), B(0, 4)

A line perpendicular to (i)

Ž 3x – 2y + l = 0

Passes through (5, 5) Ž l = – 5

Ž line is 3x – 2y = 5 …(ii)

C ŗ (5/3, 0) D ŗ (0, –5/2)

Pt. of intersection of (i) and (ii) is E(3, 2)

Ž O(0, 0), C(5/3, 0), E(3, 2), B(0, 4)

Now area of quadrilateral OCEB

= $\frac { 1 } { 2 } \left| \begin{array} { c c } 3 - 0 & 2 - 0 \\ 0 - 5 / 3 & 4 - 0 \end{array} \right|$= $\frac { 1 } { 2 } \left| \begin{array} { c c } 3 & 2 \\ - 5 / 3 & 4 \end{array} \right|$ = 23/3