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Linear Equations In Two Variables

Question
CBSEENMA9002002
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In figure, ∆PQR is an equilateral triangle with co-ordinates of vertices Q and R as (-2, 0) and (2, 0). Find the co-ordinates of the vertex P.

Solution

∵ ∆PQR is an equilateral triangle
∴ PQ = PR = QR
⇒ PQ = QR
⇒ PQ = 4
OQ = 2
In right triangle POQ,
OP2 + OQ2 = PQ2 |By Pythagoras Theorem
⇒ OP2 + (2)2 = (4)2
rightwards double arrow space space space space space space OP space equals space 2 square root of 2 therefore space space space space space space straight P space rightwards arrow space left parenthesis 0 comma space 2 square root of 3 right parenthesis

Some More Questions From Linear Equations in Two Variables Chapter

Write the answer of each of the following questions:

(i)    What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii)    What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.

See figure and write the following:

(i)     The coordinates of B.
(ii)    The coordinates of C.
(iii)   The point identified by the coordinates (-3, -5).

(iv)   The point identified by the coordinates (2, - 4).
(v)     The abscissa of the point D.
(vi)    The ordinate of the point H.
(vii)    The coordinates of the point L.
(viii)    The coordinates of the point M.

See the figure given below and write the following:

(i)     Coordinates of point A
(ii)    Abscissa of point D
(iii)   The point identified by the co-ordinates (5, 4)
(iv)   Co-ordinates of point C

A point lies on x-axis at a distance of 9 units from y-axis. What are its coordinates? What will be its coordinates if it lies on y-axis at a distance of 9 units from x-axis.

Plot the point P(2, -6) on graph paper and from it draw PM and PN as perpendiculars to x-axis and y-axis respectively. Write the coordinates of the points M and N.

In figure given below, triangle AOB with coordinates of A and O as (4, 0) and (0, 0), find the coordinates of B.

The perpendicular distance of a point from the x-axis is 2 units and the perpendicular distance from the y-axis is 3 units. Write the coordinates of the point if it lies in the:

(i) I quadrant    (ii) II quadrant
(iii)    III quadrant    (iv) IV quadrant

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

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