10th Class
Mathematics
Coordinate Geometry
Question Bank
Co-ordinate Geometry
question_answer
The extremities of the diagonal of a parallelogram are the points (3, -4) and (-6, 5).Third vertex is the point (-2, 1). Find its fourth vertex.
A) (1, 1)
B) (1, 0)
C) (0, 1)
D) (-1, 0)
Correct Answer:
D
Solution :
In parallelogram ABCD, opposite sides are equal. \[\frac{bc}{\sqrt{{{b}^{2}}+{{c}^{2}}}}\]\[\therefore \] \[=\sqrt{64+36}=10\,cm\]\[\frac{PB}{PC}=\frac{AP}{DP}\] \[\frac{PB}{PC}=\frac{AP}{DP}\]\[\Rightarrow \] ....(1) Similarly, \[x=\frac{1740}{29}=60\] \[\Rightarrow \]\[140\times 605=11\times L.C.M.\] .....(2) Now solve by substituting the points in the options. D (-1, 0) satisfies eqs. (1) and (2).