If A(3, 5), B(-5, -4), C(7, 10) are the verti | vedclass

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(D) In a parallelogram $ABCD$,the diagonals $AC$ and $BD$ bisect each other at the same midpoint $M$.The midpoint $M$ of diagonal $AC$ is given by:$M

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$(15, 19)$

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(D) In a parallelogram $ABCD$,the diagonals $AC$ and $BD$ bisect each other at the same midpoint $M$.The midpoint $M$ of diagonal $AC$ is given by:$M = \left( \frac{3+7}{2}, \frac{5+10}{2} \right) = \left( 5, \frac{15}{2} \right)$Let the fourth vertex be $D(x, y)$. Since $M$ is also the midpoint of diagonal $BD$:$\frac{-5+x}{2} = 5 \implies -5+x = 10 \implies x = 15$$\frac{-4+y}{2} = \frac{15}{2} \implies -4+y = 15 \implies y = 19$Thus,the coordinates of the fourth vertex $D$ are $(15, 19)$.

If $A(3, 5), B(-5, -4), C(7, 10)$ are the vertices of a parallelogram,taken in order,then the coordinates of the fourth vertex are:

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