Question

The mid-point of the line segment joining the points (−1, 3) and ${\displaystyle (8,\frac{3}{2})}$ is ______. 

Options

• ${\displaystyle (\frac{7}{2},-\frac{3}{4})}$

• ${\displaystyle (\frac{7}{2},\frac{9}{2})}$

• ${\displaystyle (\frac{9}{2},-\frac{3}{4})}$

• ${\displaystyle (\frac{7}{2},\frac{9}{4})}$

Answer 1

The mid-point of the line segment joining the points (−1, 3) and ${\displaystyle (8,\frac{3}{2})}$ is ${\displaystyle \underline{(\frac{7}{2},\frac{9}{4})}}$. 

Explanation:

The points are, (−1, 3) and ${\displaystyle (8,\frac{3}{2})}$ 

Using mid-point formula,

∴ (x, y) = ${\displaystyle (\frac{-1+8}{2},\frac{3+\frac{3}{2}}{2})}$

∴ (x, y) = ${\displaystyle (\frac{7}{2},\frac{9}{4})}$

So, ${\displaystyle (\frac{7}{2},\frac{9}{4})}$ is the required mid-point.