If the midpoint of the line segment joining the points

Asked by admin @ 04/08/2021 in Math viewed by 356 People

If the midpoint of the line segment joining the points P(a,b-2) and Q(-2,4) is R(2,-3),then the values of a and b

Answered by admin @ 04/08/2021

SOLUTION

GIVEN

The midpoint of the line segment joining the points P(a,b-2) and Q(-2,4) is R(2,-3)

TO DETERMINE

The values of a and b

FORMULA TO BE IMPLEMENTED

The midpoint of the line joining the

points (a, b) & (c, d) is

$= \displaystyle \sf{} \bigg( \frac{a + c}{2} \: , \frac{b + d}{2} \bigg)$

EVALUATION

Here the midpoint of the line segment joining the points P(a,b-2) and Q(-2,4) is

$= \displaystyle \sf{} \bigg( \frac{a - 2}{2} \: , \frac{b - 2 + 4}{2} \bigg)$

$= \displaystyle \sf{} \bigg( \frac{a - 2}{2} \: , \frac{b + 2}{2} \bigg)$

Now it is given that the midpoint of the line segment joining the points P(a,b-2) and Q(-2,4) is R(2,-3)

$\displaystyle \sf{} \bigg( \frac{a - 2}{2} \: , \frac{b + 2}{2} \bigg) = (2, - 3)$

Therefore

$\displaystyle \sf{} \frac{a - 2}{2} = 2 \: \: \: and\: \frac{b + 2}{2} = - 3$

Now

$\displaystyle \sf{} \frac{a - 2}{2} = 2 \: \: \: \: gives$

$\sf{}a - 2 = 4$

$\implies \sf{}a = 6$

Again

$\displaystyle \sf{} \frac{b + 2}{2} = - 3 \: \: \: gives$

$\sf{}b + 2 = - 6$

$\implies \sf{}b = - 8$

FINAL ANSWER

Hence the required values of a and b are 6 & - 8 respectively

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