On a grid map, two villages are at \(A(-7,\,4)\) and \(B(3,\,-10)\). A well is to be dug exactly halfway between them, on the straight road AB. At which point should the well be dug?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \((-2,\,-3)\)
The mid-point lies halfway between the two ends along each axis, so each coordinate is the average of the two ends: \(\left(\frac{x_1+x_2}{2},\,\frac{y_1+y_2}{2}\right)\).
x-coordinate \(\displaystyle =\frac{-7+3}{2}=\frac{-4}{2}=-2\)
y-coordinate \(\displaystyle =\frac{4+(-10)}{2}=\frac{-6}{2}=-3\)
Mid-point of AB, where the well is dug: \((-2,\,-3)\)