Prove that the points A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
Answers
Solution :-
Given Points are :- A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) .
So,
→ AB = √[(x2 - x1)² + (y2 - y1)²]
→ AB = √[(-2 - 0)² + (3 - (-1))²]
→ AB = √[(-2)² + (4)²]
→ AB = √[4 + 16]
→ AB = √20 units.
Similarly,
→ BC = √[(x2 - x1)² + (y2 - y1)²]
→ BC = √[(6 - (-2))² + (7 - (3)²]
→ BC = √[(8)² + (4)²]
→ BC = √[64 + 16]
→ BC = √80 units.
Similarly,
→ CD = √[(x2 - x1)² + (y2 - y1)²]
→ CD = √[(8 - 6)² + (3 - (7)²]
→ CD = √[(2)² + (-4)²]
→ CD = √[4 + 16]
→ CD = √20 units.
Similarly,
→ DA = √[(x2 - x1)² + (y2 - y1)²]
→ DA = √[(8 - 0)² + (3 - (-1))²]
→ DA = √[(8)² + (4)²]
→ DA = √[64 + 16]
→ DA = √80 units.
Similarly,
→ AC = √[(x2 - x1)² + (y2 - y1)²]
→ AC = √[(6 - 0)² + (7 - (-1))²]
→ AC = √[(6)² + (8)²]
→ AC = √[36 + 64]
→ AC = √100 = 10 units.
Similarly,
→ BD = √[(x2 - x1)² + (y2 - y1)²]
→ BD = √[(8 - (-2))² + (3 - (3)²]
→ BD = √[(10)² + (0)²]
→ BD = √[100 + 0]
→ BD = √100 = 10 units.
Therefore,
- AB = CD
- BC = DA
- AC = BD
- Opposite sides and Diagonals are equal.
Hence, vertices will form a rectangle.
Learn more :-
show that the points (1,1),(4,4) and (6,2) are vertices of a right angled triangle chapter 7 ncert class 10 plz no fake ...
https://brainly.in/question/19175875
Answer:
Solution :-
Given Points are :- A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) .
So,
→ AB = √[(x2 - x1)² + (y2 - y1)²]
→ AB = √[(-2 - 0)² + (3 - (-1))²]
→ AB = √[(-2)² + (4)²]
→ AB = √[4 + 16]
→ AB = √20 units.
Similarly,
→ BC = √[(x2 - x1)² + (y2 - y1)²]
→ BC = √[(6 - (-2))² + (7 - (3)²]
→ BC = √[(8)² + (4)²]
→ BC = √[64 + 16]
→ BC = √80 units.
Similarly,
→ CD = √[(x2 - x1)² + (y2 - y1)²]
→ CD = √[(8 - 6)² + (3 - (7)²]
→ CD = √[(2)² + (-4)²]
→ CD = √[4 + 16]
→ CD = √20 units.
Similarly,
→ DA = √[(x2 - x1)² + (y2 - y1)²]
→ DA = √[(8 - 0)² + (3 - (-1))²]
→ DA = √[(8)² + (4)²]
→ DA = √[64 + 16]
→ DA = √80 units.
Similarly,
→ AC = √[(x2 - x1)² + (y2 - y1)²]
→ AC = √[(6 - 0)² + (7 - (-1))²]
→ AC = √[(6)² + (8)²]
→ AC = √[36 + 64]
→ AC = √100 = 10 units.
Similarly,
→ BD = √[(x2 - x1)² + (y2 - y1)²]
→ BD = √[(8 - (-2))² + (3 - (3)²]
→ BD = √[(10)² + (0)²]
→ BD = √[100 + 0]
→ BD = √100 = 10 units.
Therefore,
AB = CD
BC = DA
AC = BD
Opposite sides and Diagonals are equal.
Hence, vertices will form a rectangle.