Two lamp posts stand at \(A(-9,\,6)\) and \(B(5,\,-2)\) on a site plan drawn on a grid. A bench is to be placed exactly halfway between the two posts, on the straight path AB. At which point should the bench be placed?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \((-2,\,2)\)
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 \(\displaystyle =\frac{-9+5}{2}=\frac{-4}{2}=-2\)
y-coordinate \(\displaystyle =\frac{6+(-2)}{2}=\frac{4}{2}=2\)
Mid-point of AB, where the bench is placed: \((-2,\,2)\)