Class 9 Exam > Class 9 Questions > A point on line y = 3x + 2 has equal ordinate...
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A point on line y = 3x + 2 has equal ordinate and abscissa, then the point will lie in
- a)I quadrant
- b)II quadrant
- c)III quadrant
- d)IV quadrant
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A point on line y = 3x + 2 has equal ordinate and abscissa, then the p...
If abscissa = ordinate, i.e, x = y then using this relation in equation of line, we have
x = 3x + 2 ⇒ x = -1
∴ Point has coordinates = (-1, -1)
Point has sign convection of (-, -)
∴ Point will lie in 3rd quadrant
x = 3x + 2 ⇒ x = -1
∴ Point has coordinates = (-1, -1)
Point has sign convection of (-, -)
∴ Point will lie in 3rd quadrant
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Community Answer
A point on line y = 3x + 2 has equal ordinate and abscissa, then the p...
Explanation:
To determine the quadrant in which the point lies, we need to consider the signs of the abscissa (x-coordinate) and ordinate (y-coordinate).
Given:
Line equation: y = 3x + 2
We are looking for a point on this line where the abscissa and ordinate are equal. Let's assume the point is (a, a).
Step 1:
Replace x with a and y with a in the equation of the line to find the value of a.
a = 3a + 2
Step 2:
Simplify the equation by combining like terms.
a - 3a = 2
-2a = 2
Step 3:
Solve for a by dividing both sides of the equation by -2.
a = -2/2
a = -1
Step 4:
Now we have the coordinates of the point: (-1, -1).
Step 5:
To determine the quadrant, we need to consider the signs of the coordinates.
- Since the x-coordinate (-1) is negative, the point lies in either the second or third quadrant.
- Since the y-coordinate (-1) is also negative, the point lies in the third quadrant.
Therefore, the correct answer is option 'C' - the point lies in the third quadrant.
To determine the quadrant in which the point lies, we need to consider the signs of the abscissa (x-coordinate) and ordinate (y-coordinate).
Given:
Line equation: y = 3x + 2
We are looking for a point on this line where the abscissa and ordinate are equal. Let's assume the point is (a, a).
Step 1:
Replace x with a and y with a in the equation of the line to find the value of a.
a = 3a + 2
Step 2:
Simplify the equation by combining like terms.
a - 3a = 2
-2a = 2
Step 3:
Solve for a by dividing both sides of the equation by -2.
a = -2/2
a = -1
Step 4:
Now we have the coordinates of the point: (-1, -1).
Step 5:
To determine the quadrant, we need to consider the signs of the coordinates.
- Since the x-coordinate (-1) is negative, the point lies in either the second or third quadrant.
- Since the y-coordinate (-1) is also negative, the point lies in the third quadrant.
Therefore, the correct answer is option 'C' - the point lies in the third quadrant.
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A point on line y = 3x + 2 has equal ordinate and abscissa, then the point will lie ina)I quadrantb)II quadrantc)III quadrantd)IV quadrantCorrect answer is option 'C'. Can you explain this answer?
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