On a graph, two-line segments, AB and CD of equal length are drawn. Which of these could be the coordinates of the points, A, B, C and D?
(a) A (-3,4) B (-1,2) and C (3,4) D (1,2) (b) A (-3, -4) B (-1,2) and C (3,4) D (1,2)
(c) A (-3,4) B (-1, -2) and C (3,4) D (1,2) (d) A (3,4) B (-1,2) and C (3,4) D (1,2)
Answers
Step-by-step explanation:
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Given : two-line segments, AB and CD of equal length
To Find : Which of these could be the coordinates of the points
A(3,4) , B(-1,2) , C(3,4) , D(1,2)
A(-3, 4) , B(-1,-2), C(3,4) , D(1,2)
A(-3,-4) , B(-1,2) , C(3,4) , D(1,2)
A(-3,4) , B(-1,2) , C(3,4), D(1,2)
Solution:
AB = CD
as length is always positive
Hence AB = CD if AB² = CD²
Distance formula between points (a , b) and ( c , d)
is √(c - a)² + ( d - b)²
Checking each option one by one
A(3,4) , B(-1,2) , C(3,4) , D(1,2)
AB² = (-1 - 3)² + (2 - 4)² = 16 + 4 = 20
CD² = (1 - 3)² + (2 - 4)² = 4 + 4 = 8
AB² ≠ CD²
A(-3, 4) , B(-1,-2), C(3,4) , D(1,2)
AB² = (-1 -(-3))² + (-2 - 4)² = 4 + 36 = 40
CD² = (1 - 3)² + (2 - 4)² = 4 + 4 = 8
AB² ≠ CD²
A(-3,-4) , B(-1,2) , C(3,4) , D(1,2)
AB² = (-1 - (-3))² + (2 - (-4))² =4 + 36 = 40
CD² = (1 - 3)² + (2 - 4)² = 4 + 4 = 8
AB² ≠ CD²
A(-3,4) , B(-1,2) , C(3,4), D(1,2)
AB² = (-1 -(-3))² + (2 - 4)² = 4 + 4 = 8
CD² = (1 - 3)² + (2 - 4)² = 4 + 4 = 8
AB² = CD²
Hence A(-3,4) , B(-1,2) , C(3,4), D(1,2) could be the coordinates of the points, A, B, C and D
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