Question

if p(x,y) is the midpoint of the line segment joining the point a(3,4) and b(4,6) also x+y =10 find the value of k​

Answer 1

SOLUTION

GIVEN

P(x,y) is the midpoint of the line segment joining the point A(3,4) and B(k,6) also x + y = 10

TO DETERMINE

The value of k

EVALUATION

Here the given points are A(3,4) and B(k,6)

Now middle point of the line segment joining the point A(3,4) and B(k,6) is

$\displaystyle \sf{ = \bigg( \frac{3 + k}{2} \:, \: \frac{4 + 6}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{3 + k}{2} \:, \: \frac{10}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \frac{3 + k}{2} \:, \: 5 \bigg)}$

Again P(x,y) is the midpoint

$\displaystyle \sf{ x =\frac{3 + k}{2} \:, \: y = 5 }$

Now P(x, y) is a point on the line x + y = 10

Therefore

$\displaystyle \sf{ \frac{3 + k}{2} + 5 = 10}$

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

$\displaystyle \sf{ \implies 3 + k= 10}$

$\displaystyle \sf{ \implies k= 7}$

FINAL ANSWER

Hence the required value of k = 7

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