Prove that the points A (1, 2), B (5, 4), C (3, 8) and D (-1, 6) are the vertices of a rectangle.
Answers
Answer:
plot the graph for these point and join it as you have plot this point you can see it will be a rectangle
Answer:
What would you like to ask?
8th
Maths
Understanding Quadrilaterals
Kinds of Quadrilateral
Show that the points A(1,2)...
MATHS
avatar
Asked on December 20, 2019 by
Jagadrupa Reddy
Show that the points A(1,2),B(5,4),C(3,8) and D(−1,6) are the vertices of a square.
EASY
Share
Study later
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