Question

Match the following with the midpoints of the line segment joining the given two points.

• A. $\left(\frac{7}{2},\frac{9}{2}\right)$
• B. $\left(\frac{9}{2},5\right)$
• C. $\left(\frac{13}{2},\frac{11}{2}\right)$
• D. $\left(2,5\right)$

Answer 1

Midpoint of a line segment joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$.

(i)A(3,4) and B(4,5). Here $x_1=3,y_1=4,x_2=4and{y}_2=5$
$\Rightarrow$$(\frac{3+4}{2},\frac{4+5}{2})$
=$(\frac{7}{2},\frac{9}{2})$

(ii)P(4,5) and Q(5,5). Here $x_1=4,y_1=5,x_2=5and{y}_2=5$
$\Rightarrow$$(\frac{4+5}{2},\frac{5+5}{2})$
=$(\frac{9}{2},\frac{10}{2})$
=$(\frac{9}{2},5)$

(iii)E(6,3) and F(7,8). Here $x_1=6,y_1=3,x_2=7and{y}_2=8$
$\Rightarrow$$(\frac{6+7}{2},\frac{3+8}{2})$
=$(\frac{13}{2},\frac{11}{2})$

(iv)M(1,2) and N(3,8). Here $x_1=1,y_1=2,x_2=3and{y}_2=8$
$\Rightarrow$$(\frac{1+3}{2},\frac{2+8}{2})$
=$(\frac{4}{2},\frac{10}{2})$
=(2,5)