Question

If the mid point of A(X,y) and B(4,7) is P (3,5) then the coordinates of A is​

Answer 1

Answer:

${\large{\pmb{\sf{★Given...}}}}$

Mid point of A(x,y) and B(4,7) is P (3,5)

${\large{\pmb{\sf{★To \: Find...}}}}$

Coordinates of A..?

${\large{\pmb{\sf{★Used \: Formula...}}}}$

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

${\large{\pmb{\sf{★Solution...}}}}$

From points:

• ${ \sf{ x_{1} = x}}$
• $\: { \sf{ y_{1} = y}}$
• $\: { \sf{ x_{2} = 4}}$
• $\: { \sf{ y_{2} = 7}}$

By substituting in formula,

${ \implies{ \sf{(3 ,5)= \bigg(\frac{x+ 4}{2} , \frac{y + 7}{2} \bigg)}} }$

finding x,

$: { \implies{ \sf{3 = \frac{x + 4}{2} }}}$

$: { \implies{ \sf{6 = x + 4}}}$

$\: : { \implies{ \sf{ x = 6 - 4}}}$

$\: : { \implies{ \bf{x = 2}}}$

finding y,

$\: : { \implies{ \sf{5 = \frac{y + 7}{2} }}}$

$\: : { \implies{ \sf{10 = y + 7}}}$

$\: : { \implies{ \sf{y = 10 - 7}}}$

$\: : { \implies{ \bf{y = 3}}}$

So, Value of (x, y) = (2, 3)

$\: {\large{\pmb{\sf{★Final \: Answer...}}}}$

Therefore,

Coordinates of A are (2, 3)