Question

Find the co-ordinate of the mid point of a line which joins P(2,-1) and Q(-3, 4):

• A. \((-\frac{1}{2},\frac{3}{2})\)
• B. \((\frac{3}{2},\frac{1}{2})\)
• C. \((\frac{2}{3},\frac{3}{2})\)
• D. \((-\frac{5}{2},-\frac{1}{2})\)

Answer 1

The Correct Option is A

To find the co-ordinate of the midpoint of a line segment joining two points \(P(2,-1)\) and \(Q(-3,4)\), we use the midpoint formula. The formula for the midpoint \(M(x, y)\) of a segment connecting points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\]

Substitute the given coordinates into the formula:

\[M = \left(\frac{2 + (-3)}{2}, \frac{-1 + 4}{2}\right)\]

Simplify each component:

\[M = \left(\frac{2 - 3}{2}, \frac{3}{2}\right) = \left(-\frac{1}{2}, \frac{3}{2}\right)\]

Thus, the coordinate of the midpoint is \((- \frac{1}{2}, \frac{3}{2})\).