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Question
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
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Solution
Using distance formula, we have
AB = `sqrt((2-5)^2+(-2-2)^2)=sqrt(9+16)=5`
BC = `sqrt((-2-2)^2+(t+2)^2)=sqrt(t^2+4t+20)`
AC = `sqrt((-2-5)^2+(t-2)^2)=sqrt(t^2-4t+53) `
Now, it is given that △ABC is right angled at B.
Using the Pythagorean theorem, we have
AB2 + BC2 = AC2
∴25+t2+4t+20=t2−4t+53 [From (1), (2) and (3)]
⇒45+4t=−4t+53
⇒8t=8
⇒t=1
Hence, the value of t is 1.
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In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
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Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
