If the area of a triangle whose vertices are (−2, 4), (2, −6) and (k, 4), (k > 0) is 35 sq.units, then the value of k is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5
The vertices (−2, 4) and (k, 4) both lie on the line y = 4, so that side is taken as the base. Since k > 0:
\(\text{base} = k - (-2) = k + 2\)
The height is the distance of (2, −6) from the line y = 4:
\(\text{height} = 4 - (-6) = 10\)
\( \displaystyle \frac{1}{2}(k + 2)(10) = 35 \)
\(k + 2 = 7,\quad k = 5\)