Question

The coordinates of two opposite vertices of a parallelogram are (4,5)&(1,3).what are the coordinates of the point of intersection of it's diagonals

Answer 1

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Answer 2

The coordinates of the point of intersection of it's diagonals is  $(\dfrac{5}{2},\4)$.

Explanation:

• The diagonals of parallelogram bisect each other .
• The point of intersection of it's diagonals is the midpoint of each diagonal.

Given : The coordinates of two opposite vertices of a parallelogram are (4,5)&(1,3).

The point of intersection of it's diagonals =  midpoint of line segment joining (4,5) & (1,3).      (1)

The midpoint of line segment joining (a,b) and (c,d) is $(\dfrac{a+c}{2},\dfrac{b+d}{2})$

∴ Midpoint of line segment joining (4,5) & (1,3) is $(\dfrac{4+1}{2},\dfrac{5+3}{2})$

∴ Midpoint of line segment joining (4,5) & (1,3) is $(\dfrac{5}{2},\4)$

From (1), The point of intersection of it's diagonals =  midpoint of line segment joining (4,5) & (1,3) is  $(\dfrac{5}{2},\4)$.

Hence, the coordinates of the point of intersection of it's diagonals is  $(\dfrac{5}{2},\4)$.

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The points b(1,3) and d(6,8) are two opposite vertices of square abcd. find the equation of diagonal ac

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