Find the co-ordinate of the mid point of a line which joins \(P(2, -1)\) and \(Q(-3, 4)\):
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\left(-\frac{1}{2},\frac{3}{2}\right)\)
The mid-point of the segment joining \((x_1,y_1)\) and \((x_2,y_2)\) lies halfway along it, so each of its coordinates is the average of the two end points’ coordinates: \(\displaystyle\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\). Here P gives the first pair and Q the second.
\(x\)-coordinate, the average of 2 and −3: \(\displaystyle\frac{2+(-3)}{2}=-\frac{1}{2}\)
\(y\)-coordinate, the average of −1 and 4: \(\displaystyle\frac{-1+4}{2}=\frac{3}{2}\)