A(-1, -1), B(-1,4), C(5, 4), D(5,-1) show that given sets of points are vertices of rectangle
Answers
Answered by
1
Answer:
We are going to find distance between sides
AB=
(5−1)
2
+(4−2)
2
=
16+4
=
20
=2
5
BC=
(3−5)
2
+(8−4)
2
=
4+16
=
20
=2
5
CD=
(−1−3)
2
+(6−8)
2
=
16+4
=
20
=2
5
DA=
(1+1)
2
+(2−6)
2
=
4+16
=
20
=2
5
∴ AB=BC=CD=DA
Now, we are going to find distance between diagonals.
AC=
(3−1)
2
+(6−2)
2
=
4+16
=
20
=2
5
BD=
(−1+5)
2
+(6−4)
2
=
16+4
=
20
=2
5
∴ AC=BD
So, here we can see distance between all sides and diagonals are equal.
∴ Points A,B,C and D are the vertices of a square.
solution
Step-by-step explanation:
Similar questions