Mathematics

Problem

The line

2x + ky - 8 = 0

meets the coordinate axes at the points

A

and

B

respectively, while

O

denotes the origin. a. (i) Express the area of

\triangle OAB

in terms of

k

only. b. (ii) If the area of

\triangle OAB

12\text{ cm}^2

, determine the possible value(s) of

k

. c. (iii) For each value of

k

obtained in part (ii), state the corresponding x-intercept and y-intercept of the line. d. (iv) For the positive value of

k

, sketch

\triangle OAB

and label the intercepts clearly.