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Co-ordinate geometry - Quant/Math - CAT 2009
Question 4 the day:
June 4, 2003
The question for the day is from the topic of Co-ordinate geometry.
- From the following choices what is the equation of a line whose x intercept is half as that of the line 3x + 4y = 12 and y intercept is twice as that of the same line.
| (1) |
3x + 8y = 24 |
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(2) |
8x + 3y = 24 |
| (3) |
16x + 3y = 24 |
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(4) |
3x + y = 6 |
Correct Answer - (4)
Solution:
Note: To find x intercept in a given equation put y = 0 in that equation and find the value for x (i.e., x-intercept).
Similarly, to find y intercept in a given equation put x = 0 in that equation and find the value for y (i.e., y-intercept).
Put y = 0 to find the x-intercept in 3x + 4y = 12, i.e., 3x + 4(0) = 12, therefore, x-intercept = 12/3 = 4.
Similarly, x = 0 to find the y-intercept in 3x + 4y = 12, i.e., 3(0) + 4y = 12, therefore, y-intercept = 12/4 = 3
Therefore, half of the x-intercept is 2 and twice the y-intercept is 6.
Now the equation of a line whose x-intercept and y-intercept is given can be written as
x/x-intercept + y/y-intercept = 1.
Therefore, equation of the line whose x-intercept is 2 and y-intercept is 6 can be written as x/2 + y/6 = 1 or 3x + y = 6.
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