10th Class
Mathematics
Coordinate Geometry
Question Bank
Co-ordinate Geometry
question_answer
The area of a parallelogram, whose vertices are (-4, -2), (-2, 6), (10, 6) and (8, -2) is
A) 32
B) 48
C) 72
D) 96
Correct Answer:
D
Solution :
Draw a parallelogram which has the vertices \[(-4,-2),\,(-2,6),(10,6)\] and \[(8,-2)\]. As we can see from the figure above that the base of the given parallelogram is equal to the distance between the points \[(-4,-2)\] and \[(8,-2)\]. \[\therefore \] Base of parallelogram \[=\sqrt{{{(-2-(-2))}^{2}}+{{(8-(-4))}^{2}}}\] \[=\sqrt{{{(0)}^{2}}+{{(8+4)}^{2}}}=\sqrt{{{(12)}^{2}}}=12\]and height h is the distance between the point \[(-2,6)\] and \[(-2,-2)\].. \[\therefore \] Height of the parallelogram, \[h=\sqrt{{{(-2-6)}^{2}}+{{(-2+2)}^{2}}}=8\] Now, Area of pa rallelogram = Base \[\times \]Height\[=12\times 8=96\]