Question

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

Answer:

y = 1.

Step-by-step explanation:

$(8 \: \: \: \: \: 3) = ( \frac{7 + 9}{2} \: \: \: \: \: \frac{5 + y}{2} ) \\ \\ 3 = \frac{5 + y}{2} \\ \\ y + 5 = 6 \\ \\ y = 1.$

Answer 2

SOLUTION

GIVEN

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

TO DETERMINE

The value of y

CONCEPT TO BE IMPLEMENTED

For the given two points $\sf{A( x_1 , y_1) \: \: and \: \: B( x_2 , y_2)}$

The midpoint of the line AB is

$\displaystyle \sf{ \bigg( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} \bigg)}$

EVALUATION

Here the given points are A(7,5) and B(9,y)

Midpoint of the line AB

$\displaystyle \sf{ = \bigg( \frac{7 + 9}{2} , \frac{5 + y}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{16}{2} , \frac{5 + y}{2} \bigg)}$

$\displaystyle \sf{ = \bigg(8 , \frac{5 + y}{2} \bigg)}$

Since P(8,3) is the mid point of the segment AB joining the points A(7,5) and B(9,y)

So by the given condition

$\displaystyle \sf{ \frac{5 + y}{2} = 3}$

$\displaystyle \sf{ \implies 5 + y = 6}$

$\displaystyle \sf{ \implies y = 6 - 5}$

$\displaystyle \sf{ \implies y = 1}$

FINAL ANSWER

Hence the required value of y = 1

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