Question

The mid point of line segment joining P ( a, b‐2 ) and Q ( ‐2, 4 ) is R ( 2, ‐3 ) then values of a and b are

Answer 1

Given:-

P = (a, b-2) = (x1, y1)

Q = (-2, 4) = (x2, y2)

R = (2, -3) = (x, y)

To find:-

value of a and b.

Solution:-

By midpoint formula

•°• x = (x1 + x2)/2

2 = (a + (-2))/2

2 = (a - 2)/2

4 = a - 2

4 + 2 = a

6 = a

And,

y = (y1 + y2)/2

-3 = [(b - 2) + 4]/2

-6 = b - 2 + 4

-6 = b + 2

-6 - 2 = b

-8 = b

The value for a and b are 6 and -8.

Answer 2

Given ,

• The mid point of line segment joining P(a , b ‐2) and Q(‐2 , 4) is R(2 , ‐3)

We know that , The mid point of line segment joining (x1, y1) and (x2, y2) is given by

$\boxed{ \sf{x = \frac{ x_{2} + x_{1} }{2} \: , \: y= \frac{ y_{2} + y_{1} }{2}}}$

Thus ,

$\sf \mapsto 2 = \frac{ - 2 + a}{2} \: , \: - 3 = \frac{4 + (b - 2)}{2} \\ \\ \sf \mapsto 4 = - 2 + a \: , \: - 6 = 2 + b \\ \\ \sf \mapsto a = 6 \: , \: b = - 8$

$\sf \therefore \underline{The \: value \: of \: a \: and \: b \: are \: 6 \: and -8}$