question_answer

The points A (8,5),\[B(-7,-5)\]and\[C(-5,5)\]are the vertices of a parallelogram, then its fourth vertex is

A)  (15, 10)          

B)  \[\left( \frac{3}{2},5 \right)\]

C)  (10, 15)           

D)  \[(-4,\text{ }5)\]

Correct Answer: C

Solution :

 Given, points A (8,5),\[B(-7,-5)\]and\[C(-5,5)\]are the vertices of a parallelogram. Let fourth vertex is\[D(x,\text{ }y)\]. We know that, diagonals of a parallelogram \[\therefore \]intersect each other at mid point \[\therefore \] \[\frac{8-5}{2}=\frac{x-7}{2}\] \[\Rightarrow \] \[3=x-7\] \[\Rightarrow \] \[x=10\] and      \[\frac{5+5}{2}=\frac{y-5}{2}\] \[\Rightarrow \] \[10=y-5\] \[\Rightarrow \] \[y=15\] \[\therefore \]Coordinates of D are (10, 15).