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Question
If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.
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Solution
As per the question
AB = AC
`⇒ sqrt((x-8)^2+(2+2)^2 ) = sqrt((x-2)^2 +(2+2)^2)`
Squaring both sides, we get
`(x-8)^2 +4^2 = (x - 2)^2 +4^2`
`⇒ x^2 -16x+64+16=x^2+4-4x+16`
`⇒ 16x-4x=64-4`
`⇒ x = 60/12=5`
Now,
`AB = sqrt((x-8)^2 +(2+2)^2)`
`= sqrt((5-8)^2 +(2+2)^2) (∵ x =2)`
`=sqrt((-3)^2 +(4)^2)`
`=sqrt(9+16) = sqrt(25)=5`
Hence, x = 5and AB = 5 units.
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Read the following passage:
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Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.
- How far is Alia's house from Shagun's house?
- How far is the library from Shagun's house?
- Show that for Shagun, school is farther compared to Alia's house and library.
OR
Show that Alia’s house, shagun’s house and library for an isosceles right triangle.
