Points on a Cartesian Plane

Q.

Define abscissa and ordinate.

Q.

Let ABCD be a square of side 2a. Find the coordinates of the vertices of this sqaure when

(i) A coincides with the origin and AB and AD are along OX and OY respectively.

(ii) The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.

Q.

The ordinate of a point is twice its abscissa. If its distance from the point (4, 3) is , then the coordinates of the point are

1. (1, 2) or (3, 6)

2. (2, 1) or (6, 3)

3. (2, 1) or (3, 6)

4. (1, 2) or (3, 5)

Q.

If 'a' is the length of one of the sides of an equilateral triangle ABC, base BC lies on x-axis and vertex B is at origin, find the coordinates of the vertices of the triangle ABC.

Q. The distance of the point (3 , -2) from the X-axis is .

1. 3 units
2. 2 units
3. -2 units

Q. If two opposite vertices of a square are (5, 4) and (1, −6), find the coordinates of its remaining two vertices.

Q.

What will be the reflection of the point (4, 5) about the X-axis, in the fourth quadrant?

1. (-4, 5)

2. (-4, -5)

3. (4, -5)

4. (4, 5)

Q.

On which axis do the following points lie?

(i) P (5, 0) (ii) Q(0 -2) (iii) R(-4, 0) (iv) S (0, 5)

Q. The slope of X-axis is 0.

1. True
2. False

Q.

The distance of a point from the $Y-axis$ is called its $y-coordinate$. True or False.

1. True
2. False

Q. The distance of the point P(3, 4) from the x-axis is

(a) 3 units
(b) 4 units
(c) 7 units
(d) 1 unit

Q. If two opposite vertices of a square are (3, 4) and (1, –1), find the coordinates of the other two vertices.

Q.

Find the point where 2x-3y = 12 cuts the x axis

Q.

The abscissa of all the points on the $y-axis$ is?

Q. Find the coordinates of the point on y-axis which is nearest to the point (–2, 5).

Q.

The distance of P(3, 4) from the x-axis is

(a) 3 units (b) 4 units (c) 5 units (d) 1 unit

Q.

In parallelogram ABCD, A(2, 3), B(6, 5) and D(4, 7). Then the coordinates of C is

1. (4, 2)

2. (8, 9)

3. (8, 7)

4. (4, 9)

Q. Question 2
The point P(- 4, 2) lies on the line segment joining the points A(-4, 6) and B(-4, -6).

Q. Which of the following points lies on the x-axis
(i) $(1,1)$
(ii) $(1,0)$
(iii)$(0,1)$
(iv)$(0,0)$
(V)$(-1,0)$
(vi)$(0,-1)$
(vii)$(4,0)$
(viii)$(0,-7)$

Q. Question 19
The point of the term (a, -a) always lies on the line:

A) x = a
B) y = -a
C) y = x​​​​​​​
D) x + y = 0​​​​​​​

Q. In which quadrant does the point (5, 6) lie?

1. $1^{st}$ Quadrant
2. $4^{th}$ quadrant
3. $3^{rd}$ quadrant
4. $2^{nd}$quadrant

Q.

Find the Y coordinates for the points which lie on y = 2x + 1, whose X coordinates are 3, 4 and 6.

Q. If (0, −3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex. [CBSE 2014]

Q. 15. The points A(3, 0) B(a, 2) and C(4, 1) are the vertices of triangle ABC right angled at vertex A.Find the value of a.

Q.

The point (2, 0) lies in both the $1^{st}$ and $4^{th}$ quadrants.

1. True

2. False

Q.

Find the point on the x-axis which is equidistant from (2, − 5) and (− 2, 9).

Q. Find the intercepts cut off by the line $x+y-1=0$ on the axes.

Q.

Write whether the following statements are True or False? Justify your answer. The coordinates of a point whose ordinate is $\frac{-1}{2}$and abscissa is $1$ are$-\frac{1}{2},1$.

1. True
2. False

Q.

Question 163(iii)

Supply the missing information for each diagram.

Q.

Solve the following:
(a) The locus of a point whose x coordinate is always 7 is the equation.
(b) Show that the point (3, 1) does not lie on the line 3x + 4y = 16. [4 MARKS]