Question

if p(x,y) is the midpoint of the line segment joining the points A(1,3) and (-2,6) then x+y is
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Answer 1

Answer:

p(x,y) = [(x1+X2)/2, (y1+y2)/2]

= [{ 1+(-2)}/2, (3+6)/2 ]

= (-1/2, 9/2)

therefore x = -1/2 and y = 9/2

x + y = -1/2 + 9/2

= (-1 + 9)/2

= 8/2

= 4

Answer 2

Given :-

P(x, y) is the mid point of the line segment joining the points A(1,3) and (-2,6).

To Find:

The value of x + y

$\underline{\bigstar{\sf{\ \ Solution: -\ \ }}}$

First we have to find the mid point of the line segment.

Let the mid point be "M".

We know that,

$\bullet\sf Mid \ point (M) =\dfrac{ (x_1 + x_2) }{2} ,\dfrac{ (y_1 + y_2)}{2}$

From the above points,

$\sf\bullet x_1 = 1 \\ \bullet\sf y_1 = 3 \\ \bullet\sf \ x_2 = -2\ \\ \bullet\sf \ y_2 = 6$

$\implies\sf ( M )=\dfrac{ [1 + (-2) ]}{2} \ ,\ \dfrac{(3 + 6)}{2}\\ \\ \implies\sf M =\dfrac{ (1 - 2) }{2}\ , \ \dfrac{ 9}{2} \\ \\ \implies\sf M = \dfrac{-1 }{2}\ ,\ \dfrac{9}{2}\\ \\ \implies\sf Mid point = \dfrac{-1}{2 }\ , \ \dfrac{9}{2}$

Now,

$\implies\sf (x + y) =\dfrac{ -1}{2 }+\dfrac{ 9}{2 }\\ \\ \implies\sf x+y= \cancel{\dfrac{8}{2}} \\ \\ \implies\sf x+y= 4$

$\underline{\sf{\therefore\ \ the \ value \ of \ x + y\ is \ 4\ units.}}$