Question

7.If P(8,3) is the mid point of the segment AB joining the points A(7,5) and B(9,y) then value of y is​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{P(8,3) is the midpoint of the segment joining the points}$

$\textsf{A(7,5) and B(9,y)}$

$\underline{\textbf{To find:}}$

$\textsf{The value of y}$

$\underline{\textbf{Solution:}}$

$\underline{\textsf{Formula used:}}$

$\mathsf{The\;midpoint\;of\;the\;line\;segment\;joining\;(x_1,y_1)\;and\;(x_2,y_2)\;is}$

$\mathsf{\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

$\textbf{Midpoint of the segment joining A and B=(8,3)}$

$\implies\mathsf{\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)=(8,3)}$

$\implies\mathsf{\left(\dfrac{7+9}{2},\dfrac{5+y}{2}\right)=(8,3)}$

$\implies\mathsf{\left(\dfrac{16}{2},\dfrac{5+y}{2}\right)=(8,3)}$

$\implies\mathsf{\left(8,\dfrac{5+y}{2}\right)=(8,3)}$

$\textsf{Equating the corresponding co-ordinates on bothsides, we get}$

$\mathsf{\dfrac{5+y}{2}=3}$

$\implies\mathsf{5+y=6}$

$\implies\mathsf{y=6-5}$

$\implies\boxed{\mathsf{y=1}}$

$\underline{\textbf{Find more:}}$

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