What are the coordinates of the points A and B in the figure below?

Open in App

Solution

Construction: Draw perpendiculars from points A and B, intersecting the x-axis at points C and D respectively.

In ΔACO:

The perpendicular distance of point A from x-axis and y-axis is 1 unit and

Therefore, the x-coordinate of point A is and the y-coordinate is 1.

Therefore, the coordinates of point A are (, 1).

We know that sum of angles forming a linear pair is 180°.

∴ ∠BOD + ∠BOA + ∠AOC = 180°

⇒ ∠BOD + 90° + 30° = 180°

⇒ ∠BOD + 120° = 180°

⇒ ∠BOD = 180° − 120° = 60°

BO = AO = 2 (Radii of the same circle)

In ΔBDO:

The perpendicular distance of point B from x-axis and y-axis isunit and 1 unit respectively.

As point B lies in the second quadrant therefore, the x-coordinate of point B is −1 and the y-coordinate is.

Therefore, the coordinates of point B are (−1, ).

Suggest Corrections

Similar questions

Q. In the given figure,

L M

is a line parallel to the

y

-axis at a distance of

3

units. What are the coordinates of the points

P, R

and

Q

Given below are the coordinates of points in a plane. Find out abscissa and ordinate of the given points.

(2,3), (4,5), (7,8), (11,15)

Q. From the figure given below write each of the following:
(i) The coordinates of point D
(ii) The abscissa of the point A
(iii) The point whose coordinates are (2, −3)
(iv) The point whose coordinates are (−3, −4)
(v) The ordinate of point E
(vi) The coordinates of B
(vii) The coordinates of F
(viii) The coordinates of the origin

Q. Find the Cartesian coordinates (drawing a figure in each case) of the points whose polar coordinates are

(5, \frac{π}{2})

Question 6
In the figure, LM is a line parallel to the y-axis at a distance of 3 units.
a. What are the coordinates of the points P, R and Q?
b. What is the difference between the abscissa of the points L and M?

Join BYJU'S Learning Program