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Question
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Options
right triangle
isosceles triangle
equilateral triangle
scalene triangle
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Solution
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a isosceles triangle.
Explanation:
Let A(– 4, 0), B(4, 0), C(0, 3) are the given vertices.
Now, distance between A(– 4, 0) and B(4, 0),
AB = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt([4 - (-4)]^2 + (0 - 0)^2`
= `sqrt((4 + 4)^2`
= `sqrt(8^2)`
= 8
Distance between B(4, 0) and C(0, 3),
BC = `sqrt((0 - 4)^2 + (3 - 0)^2`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5
Distance between A(– 4, 0) and C(0, 3),
AC = `sqrt([0 - (-4)]^2 + (3 - 0)^2`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5
∵ BC = AC
Hence, ΔABC is an isosceles triangle because an isosceles triangle has two sides equal.
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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).
