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Coordinate Geometry

Short Answer Type

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

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12. In figure, ∆ABC is an equilateral triangle with co-ordinates of B and C as B (1, 0) and C (5, 0). Find the co-ordiantes of vertex A.

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13. 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.

∵ ∆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 $rightwards double arrow space space space space space space OP space equals space 2 square root of 2 therefore space space space space space space straight P space rightwards arrow space left parenthesis 0 comma space 2 square root of 3 right parenthesis$

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

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15.

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.

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16.

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.

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17. 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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