Question

if the midpoint of a(x,y) b(4,7) p(3,5) then the coordinates of a is​

Answer 1

Answer

Given that,

P is the mid point of A and B.

According to the question,

A = (x, y)

B = (4, 7)

P = (3, 5)

To find,

The coordinates of A.

Solution,

We know that,

The mid point of the join of A(x₁, y₁) and B(x₂, y₂) is given by,

$\boxed{\bf P (x, y) = \bigg( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \bigg)}$

by substituting the values in the formula,

$\dashrightarrow\sf P (x, y) = \bigg( \dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2} \bigg)$

$\dashrightarrow\sf P (3,5) = \bigg( \dfrac{x + 4}{2}, \dfrac{y + 7}{2} \bigg)$

$\dashrightarrow \sf\dfrac{x + 4}{2} = 3$

$\dashrightarrow \sf \: x + 4= 6$

$\dashrightarrow \sf \: x = 6 - 4$

$\dashrightarrow \underline{\boxed{\sf \: x = 2}}$

$\dashrightarrow\sf \dfrac{y + 7}{2} = 5$

$\dashrightarrow\sf y + 7= 10$

$\dashrightarrow\sf y = 10 - 7$

$\dashrightarrow \underline{ \boxed{\sf y = 3}}$

Thus, the coordinates of A is (2,3).

Answer 2

Answer:

the answer os x=2 and y=7