## CO-ORDINATE GEOMETRY

**CO-ORDINATE GEOMETRY**

**9**TH

1. Find four different solutions of the equation x+2y=6.

2. Find two solutions for each of the following equations:

(i) 4x + 3y = 12

(ii) 2x + 5y = 0

(iii) 3y + 4=0

3. Write four solutions for each of the following equations:

(i) 2x + y = 7

(ii) πx + y = 9

(iii) x = 4y.

4. Given the point (1, 2), find the equation of the line on which it lies. How many such equations are there?

5. Draw the graph of the equation

(i) x + y = 7

(ii) 2y + 3 = 9

(iii) y - x = 2

(iv) 3x - 2y = 4

(v) x + y - 3 = 0

6. Draw the graph of each of the following linear equations in two variables:

(i) x + y = 4

(ii) x - y = 2

(iii) y = 3x

(iv) 3 = 2x + y

(v) x - 2 = 0

(vi) x + 5 = 0

(vii) 2x + 4 = 3x + 1.

7. If the point (3, 4) lies on the graph of the equation 3y=ax+7, find the value of ‘a’.

8. Solve the equations 2x + 1 = x - 3, and represent the solution(s) on

(i) the number line,

(ii) the Cartesian plane.

9. Draw a graph of the line x - 2y = 3. From the graph, find the coordinates of the point when

(i) x = - 5

(ii) y = 0.

10. Draw the graph of y = x and y = - x in the same graph. Also, find the coordinates of the point where the two lines intersect.

**CHAPTER 3 CO-ORDINATE GEOMETRY**9Thsharshar

**Write the correct answer in each of the following :**

1. Point (–3, 5) lies in the

(A) first quadrant (B) second quadrant

(C) third quadrant (D) fourth quadrant

2. Signs of the abscissa and ordinate of a point in the second quadrant are respectively

(A) +, + (B) –, – (C) –, + (D) +, –

3. Point (0, –7) lies

(A) on the x –axis (B) in the second quadrant

(C) on the y-axis (D) in the fourth quadrant

4. Point (– 10, 0) lies

(A) on the negative direction of the x-axis

(B) on the negative direction of the y-axis

(C) in the third quadrant

(D) in the fourth quadrant

5. Abscissa of all the points on the x-axis is

(A) 0 (B) 1(C) 2 (D) any number

6. Ordinate of all points on the x-axis is

(A) 0 (B) 1 (C) – 1 (D) any number

7. The point at which the two coordinate axes meet is called the

(A) abscissa (B) ordinate (C) origin (D) quadrant

8. A point both of whose coordinates are negative will lie in

(A) I quadrant (B) II quadrant

(C) III quadrant (D) IV quadrant

9. Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4)

(A) lie in II quadrant (B) lie in III quadrant

(C) lie in IV quadrant (D) do not lie in the same quadrant

10. If y coordinate of a point is zero, then this point always lies

(A) in I quadrant (B) in II quadrant

(C) on x - axis (D) on y - axis

11. The points (–5, 2) and (2, – 5) lie in the

(A) same quadrant (B) II and III quadrants, respectively

(C) II and IV quadrants, respectively (D) IV and II quadrants, respectively

12. If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has

(A) x coordinate = – 5 (B) y coordinate = 5 only

(C) y coordinate = – 5 only (D) y coordinate = 5 or –5

13. On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO which of the following figure is obtained?

(A) Square (B) Rectangle (C) Trapezium (D) Rhombus

14. If P (– 1, 1), Q (3, – 4), R(1, –1), S(–2, –3) and T (– 4, 4) are plotted on the graph paper, then the point(s) in the fourth quadrant are

(A) P and T (B) Q and R (C) Only S (D) P and R

15. If the coordinates of the two points are P (–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is

(A) – 5 (B) 1 (C) – 1 (D) – 2

16. If P (5, 1), Q (8, 0), R (0, 4), S (0, 5) and O (0, 0) are plotted on the graph paper, then the point(s) on the x-axis are

(A) P and R (B) R and S (C) Only Q (D) Q and O

17. Abscissa of a point is positive in

(A) I and II quadrants (B) I and IV quadrants

(C) I quadrant only (D) II quadrant only

2 MARKS QUESTIONS

1. Points A (5, 3), B (– 2, 3) and D (5, – 4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.

2. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, one vertex at the origin, the longer side lies on the x-axis and one of the vertices lies in the third quadrant.

3. Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS is a square.

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