Find the coordinates of the mid-point of the line segment joining the points 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 both axes, so each coordinate is the average of the two end values: \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\).
x-coordinate, the average of 2 and −3: \(\displaystyle\frac{2+(-3)}{2}=-\frac{1}{2}\)
y-coordinate, the average of −1 and 4: \(\displaystyle\frac{-1+4}{2}=\frac{3}{2}\)