Points on a Cartesian Plane

Q.

Point P lies on the line 3x+ 4y - 12 = 0. If X- coordinate of P is a, then its y-coordinate is ______.

1. 
2. 

3. 

4. 

Q.

Abscissa of all the points on the x-axis is:

1. $0$

2. 1

3. 2

4. Any number

Q. If abscissa is twice the ordinate of a pointP(a, a - 3), then plot the point P.

Q. What is the abscissa of the point (-3, 2)?

1. -3
2. 2
3. 3
4. None of these

Q. Write the coordinates of each of the points P, Q, R, S, T and O from the figure given.

Q. D and E are points on equal sides AB and AC of isosceles triangle respectively and B, C, E and D are concyclic points. If O is point of intersection of CD and BE, then prove that AO bisects the line segment DE

Q. Find the distance between P and S.

Q. 108. The line x+y =1 meets the lines represented by the equation y^3+6xy^2 +11x^2y- 6x^3 =0 at the points, P, Q, and R.IF O is the origin, then (OP)^2 +(OQ)^2+ (OR)^{} isequal to

Q.

State whether the statement is true or false:

For fixing a point on the graph sheet we need two coordinates.

1. True
2. False

Q. a †an gent is drawn to each of the circle x^2+y^2=4 and x^2+y^2=8. if the two †an gents are mutually perpendicular, the locus of their points of intersection is a circle, then centre of circle s

Q.

Point P lies on the line 3x+ 4y - 12 = 0. If X- coordinate of P is a, then its y-coordinate is ______.

1. $\frac{(12-3a)}{4}$

2. $\frac{(12-4a)}{3}$
3. $\frac{(12+3a)}{4}$
4. $\frac{(3a-12)}{4}$

Q.

If the coordinate axes are not perpendicular to each other but two lines are at an angle of ${60}^{\circ }$. How many coordinates will be used to represent a point?

1. 2

2. 3

3. 4

4. 1

Q.

What are quadrants?

Q. The mirror image of point P(2, 3) taken about the origin is point P'. Find the coordinates of P'.

1. $(-\sqrt{7},-3)$
2. $(-2,-\sqrt{7})$
3. $(-2,-3)$
4. (-3, -2)

Q. A point Q is formed by taking the mirror image of P(4, 5) in the x-axis. If a reflection of Q is taken in the y-axis, which quadrant will the resultant point be in?

1. Quadrant I
2. Quadrant IV
3. Quadrant I
4. Quadrant III

Q. The mirror image of point P(2, 3) taken about the origin is point P'. Find the coordinates of P'.

1. $(-\sqrt{7},-3)$
2. $(-2,-\sqrt{7})$
3. $(-2,-3)$
4. (-3, -2)

Q.

A line intercepts the x axis at (-7, 0), so its x intercept is

1. 7

2. ⁷/_²

3. -7

4. -⁷/_²

Q.

The x coordinate of point C is ​​​.

Q. 21. (0, 0), (3, 3) and (0, 2\sqrt3) are the three verticesof a triangle. The distance between the orthocentreand the circumcentre of the triangle is equal to(in units) (1) 2\sqrt3 (2) \sqrt3 (3)\sqrt6 (4) 0

Q.

In the figure below, is any side of ΔABC parallel to X axis? If so, the side is___ .

Q. Write the coordinates of each of the points P, Q, R, S, T and O from the figure given.

Q.

What is the x coordinate of point C?

Q. The ordinate of any point on the 𝑥-axis is _____.

1. 0
2. 1
3. 2
4. -1

Q. What will be solution of the lines x = 3 and y = 4?

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

Q. check weather the points (1, 5), (0, 3) lie on the line y =3 +2x or not

Q.

How do you determine the quadrant in which $-1$ radians lies?

Q. With reference to figure, see which quadrants or axes do the points L, M, N, K, G, B, R, T and D belong, and find the sum of the abscissa of all the marked points.

Q. Find the distance between P and S.

Q. Fill in the blanks with suitable words:
If a point $(x,y)$ lies above horizontal axis, then $y$ is always __________.

Q. Which of the following equations represents a line parallel to the 𝑥−axis?

1. 𝒚 = 𝟐𝒙
2. 𝒚 = −𝟐
3. 𝒙 = 𝟓
4. 𝒚=𝟑𝒙 − 𝟏