Question

The co-ordinates of the midpoint P of segment AB with A $\equiv$ (3.5, 9.5), B $\equiv$ $(-1.5,0.5)$ is $(1,a)$, then the value of a is _____

Answer 1

$Lettheco-ordinatesofthepointPbeP(x,y)whichbisectsthelinesegmentABjoiningthepointsA(x_1,y_1)=(3.5,9.5)\&B(x_2,y_2)=(-1.5,0.5)Then,bythesectionformula,x=\frac{x_1+x_2}{2}=\frac{3.5+(-1.5)}{2}=1andy=\frac{y_1+y_2}{2}=\frac{9.5+0.5}{2}=5$

$\therefore P(x,y)=P(1,5)$

$P(x,y)=P(1,5).$

$\therefore P(1,a)=P(1,5)$

$⟹a=5$