Question

In figure, ∆ABC and ∆ABD are equilateral triangles. Find the coordinates of points C and D.

Solution

∵ ∆ABC is an equilateral triangle
∴AC = BC = AB
⇒ BC = AB
⇒ BC = 2a
In right triangle COB,
OB² + OC² = BC²
$rightwards double arrow space space$ a² + OC²= (2a)2
$rightwards double arrow$ OC² + 3a²
$rightwards double arrow$ $OC space equals space square root of 3 space straight a$
$therefore space space space space space space space space space space straight C rightwards arrow space space left parenthesis 0 comma space square root of 3 space straight a right parenthesis$
Similarly, $straight D space rightwards arrow space left parenthesis 0 comma space minus square root of 3 space straight a right parenthesis$

Some More Questions From Linear Equations in Two Variables Chapter

In figure, ABCD is a square. Find the co-ordinates of points A and D.

In figure, write the co-ordinates of the points P, Q, R and S.

Find the co-ordinates of a point:

(i) whose ordinate is 6 and lies on y-axis.
(ii) whose abscissa is -3 and lies on x-axis.

In which quadrant, can a point have:
(i) abscissa equal to its ordinate
(ii) ordinate equal in magnitude to abscissa
(iii) ordinate equal and opposite of abscissa
(iv) abscissa twice that of the ordinate.

See figure and complete the following statements:

(i)    The abscissa and the ordinate of the point B are _ _ _ and _ _ _, respectively. Hence the coordinates of B are (_ _, _ _).
(ii)    The x-coordinate and the y-coordinate of the point M are _ _ _ and _ _ _, respectively. Hence the coordinates of M are (_ _ _, _ _ _).
(iii)    The x-coordinate and the y-coordinate of the point L are _ _ _ and _ _ _, respectively. Hence the coordinates of L are (_ _, _ _).
(iv)    The x-coordinate and the y-coordinate of the point S are _ _ _ and _ _ _, respectively. Hence the coordinates of S are (_ _, _ _).

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Linear Equations In Two Variables

In figure, ∆ABC and ∆ABD are equilateral triangles. Find the coordinates of points C and D.

Some More Questions From Linear Equations in Two Variables Chapter

In figure, ABCD is a square. Find the co-ordinates of points A and D.

In figure, write the co-ordinates of the points P, Q, R and S.

Find the co-ordinates of a point:

(i) whose ordinate is 6 and lies on y-axis.
(ii) whose abscissa is -3 and lies on x-axis.

In which quadrant, can a point have:
(i) abscissa equal to its ordinate
(ii) ordinate equal in magnitude to abscissa
(iii) ordinate equal and opposite of abscissa
(iv) abscissa twice that of the ordinate.

In which quadrant do the given points lie?

(a) (2, -1) (b) (-1, 7)

(c) (-2, -3) (d) (4, 5)

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Linear Equations In Two Variables

In figure, ∆ABC and ∆ABD are equilateral triangles. Find the coordinates of points C and D.

Some More Questions From Linear Equations in Two Variables Chapter

In figure, ABCD is a square. Find the co-ordinates of points A and D.

In figure, write the co-ordinates of the points P, Q, R and S.

Find the co-ordinates of a point: (i) whose ordinate is 6 and lies on y-axis.(ii) whose abscissa is -3 and lies on x-axis.

In which quadrant, can a point have:(i) abscissa equal to its ordinate(ii) ordinate equal in magnitude to abscissa(iii) ordinate equal and opposite of abscissa(iv) abscissa twice that of the ordinate.

In which quadrant do the given points lie? (a) (2, -1) (b) (-1, 7) (c) (-2, -3) (d) (4, 5)

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the co-ordinates of a point:

(i) whose ordinate is 6 and lies on y-axis.
(ii) whose abscissa is -3 and lies on x-axis.

In which quadrant, can a point have:
(i) abscissa equal to its ordinate
(ii) ordinate equal in magnitude to abscissa
(iii) ordinate equal and opposite of abscissa
(iv) abscissa twice that of the ordinate.

In which quadrant do the given points lie?

(a) (2, -1) (b) (-1, 7)

(c) (-2, -3) (d) (4, 5)