10th Class
Mathematics
Coordinate Geometry
Question Bank
Co-ordinate Geometry
question_answer
Area of the rectangle whose vertices are (-2 5) (8, 5), (8,-2) and (-2,-2) is
A) 45
B) 50
C) 55
D) 70
Correct Answer:
D
Solution :
Let us draw a rectangle which has given vertices. Here, length of the rectangle will be the distance. By the distance formula distance between \[(-2,-2)\] and \[(8,-25)\] \[=\sqrt{{{(-2-(-2))}^{2}}+{{(8-(-2))}^{2}}}\] \[=\sqrt{{{(0)}^{2}}+{{(8+2)}^{2}}}\] \[=\sqrt{{{(10)}^{2}}}\] \[=10.\] So, length of the rectangle is 10 and the distance between the points \[(8,-2)\] and \[(8,5)\] will be the width of the rectangle. \[\Rightarrow \]Width of rectangle \[=\sqrt{{{(5-(2))}^{2}}+{{(8-8)}^{2}}}\] \[=\sqrt{{{(5+2)}^{2}}}\] \[=\sqrt{{{(7)}^{2}}}\] \[=7.\] Now, area of rectangle is given by the product of its length and width between points \[(-2,-2)\] and \[(8,-2)\] \[\therefore \] Area of rectangle with given vertices\[=Length\times Width=10\times 7=70\]