Two Dimensional Analytical Geometry Practical Problems for Grade 11 :
Here we are going to see some practical problems in two dimensional analytical geometry.
Question 1 :
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time shown in the following table.
Weight, (kg) 2 4 5 8
Length, (cm) 3 4 4.5 6
(i) Draw a graph showing the results.
(ii) Find the equation relating the length of the spring to the weight on it.
(iii) What is the actual length of the spring.
(iv) If the spring has to stretch to 9 cm long, how much weight should be added?
(v) How long will the spring be when 6 kilograms of weight on it?
Solution :
(ii) To find the linear relation, let us take two point on the line.
(2, 3) (4, 4)
Equation of the line :
(y−y_{1})/(y_{2}−y_{1}) = (x−x_{1})/(x_{2}-x_{1})
(y−3)/(4-3) = (x−2)/(4-2)
(y−3)/1 = (x−2)/2
2(y - 3) = x - 2
2y - 6 = x - 2
x - 2y - 2 + 6 = 0
x - 2y + 4 = 0
Here "x" stands for weight and "y" stands for length.
(iii) To find the actual length of spring, we have to put x = 0 and find the value of y.
-2y + 4 = 0
y = 2 cm
(iv) If length of spring (y) = 9 cm, then x = ?
x - 2(9) + 4 = 0
x - 18 + 4 = 0
x = 14 kg
(v) If x = 6 kg, then y = ?
x - 2y + 4 = 0
6 - 2y + 4 = 0
10 - 2y = 0
2y = 10
y = 5 cm
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