Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area. [3 MARKS]
Formula: 1 Mark
Application: 1 Mark
Answer: 1 Mark
Let A (0 , -1) , B (6 , 7) , C ( -2 ,3) and D (8 , 3) be the given points. Then,
AB=√(6−0)2+(7+1)2=√36+64=10
CD=√(8+2)2+(3−3)2=√100+0=10
AD=√(8−0)2+(3+1)2=√64+16=4√5
BC=√(6+2)2+(7−3)2=√64+16=4√5
∴ AB = CD and AD = BC
So, ABCD is a parallelogram
Now , AC=√(−2−0)2+(3−(−1)2=√4+16=2√5
and , BD=√(8−6)2+(3−7)2=√4+16=2√5
Clearly, opposite sides are equal and diagonals are equal
.
Hence, ABCD is a rectangle.
Now, Area of rectangle ABCD=AB×BC
AB×BC=10×4√5 sq.units
⇒AB×BC=40√5 sq.units