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If (a, b) is the mid-point of the line segment joining the points A $(10,-6)$, B(k,$4$) and a$-2b=18$, find the value of k and the distance AB.
If (a, b) is the mid-point of the line segment joining the points A $(10,-6)$, B(k,$4$) and a$-2b=18$, find the value of k and the distance AB.
CBSE | Class 10 | Co-ordinate Geometry | Exercise 14.3 | Maths | RD Sharma
If (a, b) is the mid-point of the line segment joining the points A $(10,-6)$, B(k,$4$) and a$-2b=18$, find the value of k and the distance AB.

As it is given (a, b) is the mid-point of the line segment A($10,-6$) and B(k,$4$)

Therefore,

(a, b) $=(10+k/2,-6+4/2)$

a $=(10+k)/2$ and b $=-1$

$2a=10+k$

$K=2a–10$

Given that, $a–2b=18$

By Using $b=-1$ in the above relation we get,

$a-2(-1)=18$

A$=18-2=16$

So,

k $=2(16)-10=32-10=22$

Hence, $AB=\sqrt{\left[ {{(22-10)}^{2}}+{{(4+6)}^{2}} \right]}$

$=\sqrt{\left[ {{(12)}^{2}}+{{(10)}^{2}} \right]}$

$=\sqrt{\left[ 144+100 \right]}$

$=2\sqrt{61}$

i

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