22 questions · timed · auto-graded
Solution:
Since, x co-ordinate is negative and y co-ordinate is positive, the given point lies in Quadrant II.
Solution:
The ordinate (y co-ordinate) of every point on the x-axis is 0.
Solution:
A point both of whose coordinates are negative, that is, of the from (-, -) lies in quadrant III.
Solution:
The point at which the two coordinate axes meet is called the origin.
Solution:
Absissa of a point is positive when the points are of the form (+, +) and (+, -).
So, the absissa of the point is positive in quadrant I and IV.
Solution:
By plotting the given points, we find that figure OABC is a rectangle.
Solution:
For the point to lie on the line y = 3x + 4, it has to satisfy the equation of the line.
Putting x = 1, in y = 3x + 4, we get y = 3(1) + 4 ⇒ y = 7
So, the point satisfies the equation and hence lies on the given line.
Putting x = 2, in y = 3x + 4, we get y = 3(2) + 4 ⇒ y = 10
So, the point satisfies the equation and hence lies on the given line.
Putting x = 1, in y = 3x + 4, we get y = 3(-1) + 4 ⇒ y = 1
So, the point satisfies the equation and hence lies on the given line.
Putting x = 4, in y = 3x + 4, we get y = 3(4) + 4 ⇒ y = 16
But y = 12.
So, the point not satisfy the equation and hence lies on the given line.
Solution:
Point (-7, 0) lies on negative direction of the x-axis as its x co-ordinate is negative and y co-ordinate is zero.
Solution:
Clearly, $\triangle\text{AOB}$ is a right-angled triangle.
$\therefore$ Area of $\triangle\text{AOB}=\frac{1}{2}\times\text{Base}\times\text{Height}$
$=\frac{1}{2}\times\text{OB}\times\text{OA}$
$=\frac{1}{2}\times6\times6$
= 18 square units.
Solution:
Points (1, -1), (2, -2) and (4, -5) lie in Quadrant IV, but point (-3, -4) lies in Quadrant III.
Hence, all the given points do not lie in the same quadrant.
Solution:
Since, both the coordinates of given point are negative, it lies in Quadrant III.
Solution:
The points are same when they are of the form (m, m) or (-n, -n).
This happens only in quadrant I and quadrant III.
So, the points (other than the origin) for which the abscissa is equal to the ordinate lie in quadrant I and quadrant III.
Solution:
Abscissa of A - Abscissa of B
= -2 - (-3)
= -2 + 3
= 1
Solution:
The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is (0, -5).
Solution:
For the point to lie on the line y = 2x + 3, it has to satisfy the equation of the line.
Putting x = 2, in y = 2x + 3, we get y = 2(2) + 3 ⇒ y = 7
But y = 8.
So, the point does not satisfy the equation and hence does not lie on the given line.
Putting x = 3, in y = 2x + 3, we get y = 2(3) + 3 ⇒ y = 9
So, the point satisfies the equation and hence lies on the given line.
Putting x = 4, in y = 2x + 3, we get y = 2(4) + 3 ⇒ y = 11
But y = 12.
So, the point does not satisfy the equation and hence does not lie on the given line.
Putting x = 5, in y = 2x + 3, we get y = 2(5) + 3 ⇒ y = 13
But y = 15.
So, the point does not satisfy the equation and hence does not lie on the given line.
Solution:
Points of the type (+, -) lie in the 4th quadrant.
Since x > 0 and y < 0, the point (x, y) lies in quadrant IV.
Solution:
If the y-coordinate of a point is zero then this point always lies on the x-axis.
Solution:
For point (-5, 3), the x co-ordinate is negative and the y co-ordinate is positive. Hence, it lies in Quadrant II.
For point (3, -5), the x co-ordinate is positive and the y co-ordinate is negative. Hence, it lies in Quadrant IV.
Solution:
If a point lies on y-axis, then its abscissa is 0.
Hence, the point whose ordinate is 3 and which lies on the y-axis is (0, 3).
Solution:
Point (0, -8) lies on y-axis as its x co-ordinate is 0.
Solution:
The abscissa of point (0, 3) is 0. Hence, it lies on y-axis.
Solution:
The perpendicular distance of the point A(3, 4) from the y-axis is 3 units.