Question

please answer this question​

Answer 1

QUESTION :–

• C is the mid-point of PQ , If P(4,x) , C is (y,-1) and Q(-2,4) , then 'x' and 'y' respectively are –

(a) -6 and 1

(b) -6 and 2

(c) 6 and 1

(d) 6 and -2

ANSWER :–

GIVEN :–

• C is the mid-point of PQ , If P(4,x) , C is (y,-1) and Q(-2,4) .

TO FIND :–

• Value of x and y = ?

SOLUTION :–

• We know that if two points A(a,b) and B(c,d) , then mid-point –

$\\ \dashrightarrow\bf \: \: Mid - point = \left( \dfrac{a + c}{2} ,\dfrac{b + d}{2} \right)$

• So that –

$\\ \implies \bf \: \: Mid - point = \left( \dfrac{4 - 2}{2},\dfrac{x - 4}{2} \right)$

$\\ \implies \bf \: \: (y,1) = \left( \dfrac{4 - 2}{2},\dfrac{x - 4}{2} \right)$

$\\ \implies \bf \: \: (y,1) = \left( \dfrac{2}{2},\dfrac{x - 4}{2} \right)$

$\\ \implies \bf \: \: (y,1) = \left( 1,\dfrac{x - 4}{2} \right)$

• Now Let's compare –

$\\ \implies \large{ \boxed{ \bf y=1}}$

• And –

$\\ \implies \bf \dfrac{x - 4}{2} = 1$

$\\ \implies \bf x - 4 = 2$

$\\ \implies \bf x = 4+ 2$

$\\ \implies \large{ \boxed{\bf x =6}}$

▪︎Hence , Option (c) is correct.