Maths M.C.Q

4. Q and O

Solution:

We now that, a point lies on X-axis, if its y-coordinate is zero.

So, the points on the axis are Q(8, 0) and O(0, 0).

4. In the fourth quadrant.

Solution:

In Point (0, -7) co-ordinate of x axis is zero so it lies on y axis.

3. II and IV quadrants, respectively.

Solution:

In point (-5, 2), x-coordinate is negative and y-coordinate is positive, so it lies in II quadrant and in point (2, -5), x- coordinate is positive and y-coordinate is negative, so it lies in IV quadrant.

4. y coordinate = 5 or -5

Solution:

We do know that perpendicular distance of a point from the X-axis Y-coordinate of that point. Here foot of perpendicular lies on the negative direction of X-axis, so perpendicular distance can be measure in II quadrant or III quadrant. Hence, the point P has y coordinate = 5 or -5

4. Any number.

Solution:

Abscissa of all the points on the X-axis is any number because X-axis is a number line which contains many real numbers on it.

1. 3

Solution:

The perpendicular distance of the point P(3, 4) from the y-axis is abscissa (x-coordinate) of the point (3, 4), which is 3.

1. 0

Solution:

Ordinate of all the points on the x-axis is 0.Because ordinate (or y-coordinate) of a point is perpendicular distance of this point from the x-axis measured along the y–axis.

2. Rectangle.

Solution:

Here, point O(0, 0) is the origin. A(3, 0) lies on positive direction of X-axis, B(3, 4) lies in 1^st quadrant and C(0, 4) lines on positive direction of Y-axis. On joining OA AB, BC and CO the figure obtained is a rectangle.

2. (-2, 4)

Solution:

Here, given point P lies in II quadrant, so its abscissa will be negative and ordinate will be positive. Also its perpendicular distance from X-axis is 4 y-coordinate of P is 4 and its perpendicular distance from Y-axis is 2. So, x–coordinate is -2. Hence, coordinate of P are (-2, 4).

2. 1

Solution:

We have, points P(-2, 3) and Q(-3, 5)

Here, abscissa of P i.e., x-coordinate of P is -2 and abscissa of Q i.e., x-coordinate of Q is -3.

So, (Abscissa of P) - (Abscissa of Q)

= -2 - (-3) = -2 + 3 = 1

2. (0, 4)

Solution:

Given ordinate of the point is 4 arid the point lies on Y-axis, so its abscissa is zero. Hence, the required point is (0, 4).

3. Origin.

Solution:

The points at which the two coordinate axes meet is called the origin.

2. Second quadrant.

Solution:

In the point (-3, 5) abscissa is negative and ordinate is positive. So, it lies in the second quadrant.

1. T

Solution:

Clearly, point T lies in the fourth quadrant. The distance of T from y-axis is 3 unit and from x-axis is -5 units. So, the points identified by the coordinate (-5, 3) is T.

4. Do not lie in the same quadrant.

Solution:

In points (1, -1), (2, -2) and (4, -5) x-coordinate is positive and y-coordinate is negative, So, they all lie in IV quadrant. In point (-3, -4) x-coordinate is negative and y-coordinate is negative. So, it lies in III quadrant. So, given points do not lie in the same quadrant.

3. (0, -5)

Solution:

Given the point lies on Y-axis this shows that this x-coordinate is zero. Also it is at a distance of 5 units in negative direction of Y-axis, so its y–coordinate is negative. Hence, the required point is (0, -5).

1. On the negative direction of the x-axis.

Solution:

In point (-10, 0) y-coordinate is zero, so it lies on X-axis and its x-coordinate is negative, so the point (-10, 0) lies on the X-axis in the negative direction.

3. III quadrant.

Solution:

A point both of whose coordinates are negative will lie in III quadrant because, in III quadrant x-coordinate and y-coordinate both are negative.

2. Q and R

Solution:

We know that quadrant IV consists of the all points (x, y) for which x is positive and y negative. So, the points in the fourth quadrants are Q(3, -4) and R(1, -1).

2. I and IV quadrants.

Solution:

Abscissa of a point is positive in I and IV quadrants.

3. -, +

Solution:

Signs of the abscissa and ordinate of a point in the second in the second quadrant a-, +

3. P, R and T.

Solution:

We know that, if a point is of the form (x, 0) i.e., its y-coordinate is zero, then it will lie on X-axis otherwise not. Here, y-coordinates of points P(0, 3), R(0, -1) and T(1, 2) are not zero, so these points do not lie on the X-axis.

3. On x-axis.

Solution:

We know that if y-coordinate of a point, i.e., ordinate is zero, then this point always lies on x-axis.

4. II and IV quadrants.

Solution:

The points whose abscissa and ordinate have different sings will be of the from (-x, y) or (x, -y) and these points will lie in II and IV quadrants.