in the diagram below points A and B are 3 inches apart try to find two points that are 1 inch from point A and 1.5 inches from B why do you think it is impossible to find such points
Answers
Given : points A and B are 3 inches apart
To find : points that are 1 inch from point A and 1.5 inches from B
Solution:
A and B are 3 inches apart
=> AB = 3 inch
points 1 inch from point A and 1.5 inches from B
Let say Point is C
would Either be colinear or form a Triangle with Ab
Case 1 : colinear
AC = 1 inch
BC = 1.5nch
AB = 3 inch
As per segment addition postulate
1 + 1.5 inch should equal to 3 inch
Hence colinear point is not possible
Case 2 : Form a triangle
AC = 1 inch
BC = 1.5nch
AB = 3 inch
in triangle sum of any two sides > third side
but 1 + 1.5 = 2.5 inch < 3 inch
Hence triangle is not possible
Hence such point can not exist.
so impossible to find such points
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