in the figure ABCD is a square. A(2,3) and B (5,3) ,AB is parallel to x axis if, What is the length of side of the square What is the coordinates of C and D?
Answers
Answer:
Step-by-step explanation:
(a) Distance between A and B = |4 - 0| = 4
Since the opposite sides of a parallelogram are equal, the distance between C and D is also 4.
Also, the y-coordinates of A and B are equal, the side AB is parallel to the x-axis. And, since ABCD is a parallelogram, CD is also parallel to the x-axis. So the y-coordinates of C and D are also equal.
Thus, the x-coordinate of D = 8 - 4 = 4
Hence, the coordinates of D are (4, 5).
(b) The x-coordinates of D and B are equal. So the line BD is parallel to the y-axis or BD is perpendicular to the x-axis.
So, height of the parallelogram =DB=∣y
1
−y
2
∣=∣5−2∣=∣3∣=3
(c) BC=
(x
1
−x
2
)
2
+(y
1
−y
2
)
2
=
(8−4)
2
+(5−2)
2
=
(4
2
)+(3)
2
=
16+9
=
25
= 5 units
AD = BC = 5 units
Perimeter =2×(4+5)=18 units
Area=Base×Height=4×3=12sq.units.