Question

If the mid point of the line segment joining A(x/2,y+1/2)and (x+1,y-3) is C(5,-2) find xy

Answer 1

Answer: The value of x= 6 and y = $\frac{-3}{4}$

Step-by-step explanation:

Since we have given that

Coordinates of A is given by

$(\frac{x}{2},y+\frac{1}{2})$

Coordinates of B is given by

$(x+1,y-3)$

And the midpoint of AB is 'C' with coordinates $(5,-2)$

As we know the formula for "Mid point ":

$(\frac{\frac{x}{2}+x+1}{2},\frac{y+\frac{1}{2}+y-3}{2})=(5,-2)\\\\(\frac{x+2x+2}{4},\frac{2y+1+2y-6}{4})=(5,-2)\\\\(\frac{3x+2}{4},\frac{4y-5}{4})=(5,-2)\\\\\text{ equating coordinate wise}\\\\\frac{3x+2}{4}=5,\frac{4y-5}{4}=-2\\\\3x+2=20\\\\3x=20-2=18\\\\x=\frac{18}{3}=6\\\\and\\\\4y-5=-8\\\\4y=-8+5\\\\4y=-3\\\\y=\frac{-3}{4}$

Hence, The value of x= 6 and y = $\frac{-3}{4}$

Answer 2

Since we have given that

Coordinates of A is given by

(\frac{x}{2},y+\frac{1}{2})(

2

x

,y+

2

1

)

Coordinates of B is given by

(x+1,y-3)(x+1,y−3)

And the midpoint of AB is 'C' with coordinates (5,-2)(5,−2)

As we know the formula for "Mid point ":

\begin{gathered}(\frac{\frac{x}{2}+x+1}{2},\frac{y+\frac{1}{2}+y-3}{2})=(5,-2)\\\\(\frac{x+2x+2}{4},\frac{2y+1+2y-6}{4})=(5,-2)\\\\(\frac{3x+2}{4},\frac{4y-5}{4})=(5,-2)\\\\\text{ equating coordinate wise}\\\\\frac{3x+2}{4}=5,\frac{4y-5}{4}=-2\\\\3x+2=20\\\\3x=20-2=18\\\\x=\frac{18}{3}=6\\\\and\\\\4y-5=-8\\\\4y=-8+5\\\\4y=-3\\\\y=\frac{-3}{4}\end{gathered}

(

2

2

x

+x+1

,

2

y+

2

1

+y−3

)=(5,−2)

(

4

x+2x+2

,

4

2y+1+2y−6

)=(5,−2)

(

4

3x+2

,

4

4y−5

)=(5,−2)

equating coordinate wise

4

3x+2

=5,

4

4y−5

=−2

3x+2=20

3x=20−2=18

x=

3

18

=6

and

4y−5=−8

4y=−8+5

4y=−3

y=

4

−3

Hence, The value of x= 6 and y = \frac{-3}{4}

4

−3