Class 9: Co-ordinate Geometry – Exercise 19.1 – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: Write down the coordinates of each of the points $P, Q, R, S, T, U$ and $V$ shown in the adjoining graph.

Answer:

$P(2,3), Q(-3, 2), R(-2, -3), S(4, -2), Y(2, 0), V(-3, 0), U(0, -2)$

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Question 2: Plot the following points in rectangular coordinate system. In which quadrant do they lie? i) $P (5, 7)$ (ii) $Q (-3, 4)$ (iii) $R (- 2, - 5)$ (iv) $S (2, - 7)$ (v) $T (- 2,0)$ (vi) $U(0,7)$ (vii) $V(0,-4)$ (vii) $W(-3,-3)$ .

Answer:

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Question 3: On which axis do the following points lie? (i) $P (5,0)$ (ii) $Q (0, - 2)$ (iii) $R (- 4, 0)$ (iv) $S (0,5)$

Answer:

(i) $P (5,0) - Lies \ on \ y-axis$ (ii) $Q (0, - 2) - Lies \ on \ x-axis$

(iii) $R (- 4, 0) - Lies \ on \ y-axis$ (iv) $S (0,5) - Lies \ on \ y-axis$

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Question 4: Plot the points $(- 2, 0), (2, 0), (2, 2), (0, 4), (- 2, 2)$ and join them in order. What figure do you get?

Answer:

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Question 5: Let $ABCD$ be a square of side $2a$ . Find the coordinates of the vertices of this Square when

(i) $A$ coincides with the origin and $AB$ and $AD$ are along $OX$ and $OY$ respectively.

(ii) The center of the square is at the origin and coordinate axes are parallel to the sides $AB$ and $AD$ respectively.

Answer:

ii)

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Question 6: The base $PQ$ of two equilateral triangles $PQR$ and $PQR'$ with side $2a$ lies along $Y$ axis such that the mid-point of $PQ$ is at the origin. Find the coordinates of the vertices $R$ and $R'$ of the triangles.

Answer:

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Question 7: Draw the quadrilateral whose vertices are:

(i) $P (1, 1), Q(2,4), R(8,4)$ and $S (10,1)$

(ii) $A (-2, 2), B (- 4, 2), C (- 6,- 2)$ and $D (- 4, - 2)$

(iii) $P (1, 4), Q(-5, 4), R(-5,- 3)$ and $S (1,-3)$

Name the type of quadrilateral so formed in each case.

Answer:

ii)

iii)

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Question 8: Plot the points $O (0, 0), P (4,0)$ and $Q (2, 6)$ in a rectangular coordinate system. Mark midpoint of $OP$ as $L$ . Write its coordinates. Draw the median of $\triangle OPQ$ passing through $Q$ and write the coordinates of its centroid.