Question

J(3, 4), K(8, 9), and L(6, 7) are the midpoints of the sides AB, BC, and AC respectively of $\Delta ABC$. The coordinates of C are:

• A. (5, 6)
• B. (7, 8)
• C. (1, 2)
• D. (11, 12)

Answer 1

The correct option is D (11, 12)

From Mid-point theorem, we conclude that JLCK is a parallelogram.
Thus, midpoint of JC = midpoint of KL
[Diagonals of a parallelogram bisect each other]
Let the coordinates of C be (x, y).
Thus, by midpoint formula, we have:
$\frac{3+x}{2}=\frac{8+6}{2}and\frac{4+y}{2}=\frac{9+7}{2}$
$\Rightarrow x=11,y=12$

Hence, the coordinates of C are (11, 12).