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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.6

Multiple Choice Questions :

Question 1.

If the y-coordinate of a point is zero, then the point always lies

(1) in the I quadrant

(2) in the II quadrant

(3) on x-axis

(4) on y-axis

Solution:

(3) on x-axis

Question 2.

The points (-5, 2) and (2, -5) lie in the ___.

(1) same quadrant

(2) II and III quadrant respectively

(3) II and IV quadrant respectively

(4) IV and II quadrant respectively

Hint: (-, +) lies II^{nd} quadrant and (+, -) lies in IV^{th} quadrant

Solution:

(3) II and IV quadrant respectively

Question 3.

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

(1) Square

(2) Rectangle

(3) Trapezium

(4) Rhombus

Hint: In trapezium one pair of opposite side is parallel.

Solution:

(3) Trapezium

Question 4.

If P(-1, 1), Q(3, -4), R(1, -1), S(-2, -3) and T(-4, 4) are plotted on a graph paper, then the points in the fourth quadrant are ____.

(1) P and T

(2) Q and R

(3) only S

(4) P and Q

Hint: Points in IVth quadrant are (+, -)

Solution:

(2) Q and R

Question 5.

The point whose ordinate is 4 and which lies on they-axis is

(1) (4, 0)

(2) (0, 4)

(3) (1, 4)

(4) (4, 2)

Hint: Points in y-axis have abscissa a zero

Solution:

(2) (0, 4)

Question 6.

The distance between the two points (2, 3) and (1, 4) is ___ .

(1) 2

(2) \(\sqrt{56}\)

(3) \(\sqrt{10}\)

(4) \(\sqrt{2}\)

Hint: Distance = \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\)

Solution:

(4) \(\sqrt{2}\)

Question 7.

If the points A (2, 0), B (-6, 0), C (3, a – 3) lie on the x-axis then the value of a is ___.

(1) 0

(2) 2

(3) 3

(4) -6

Hint: Points in y-axis have ordinate zero. ∴ a – 3 = 0 ⇒ a = 3

Solution:

(3) 3

Question 8.

If ( x + 2, 4) = (5, y – 2), then the coordinates (x, y) are ___.

(1) (7, 12)

(2) (6, 3)

(3) (3, 6)

(4) (2, 1)

Hint: x + 2 = 5 ⇒ x = 3; y – 2 = 4 ⇒ y = 6

Solution:

(3) (3, 6)

Question 9.

If Q_{1}, Q_{2}, Q_{3}, Q_{4} are the quadrants in a Cartesian plane then Q_{2} ∩ Q_{3} is

(1) Q_{1} ∪ Q_{2}

(2) Q_{2} ∪ Q_{3}

(3) Null set

(4) Negative x-axis

Hint: Quadrants do not contain the axis.

Solution:

(3) Null set

Question 10.

The distance between the point (5, -1) and the origin is

(1) \(\sqrt{24}\)

(2) \(\sqrt{37}\)

(3) \(\sqrt{26}\)

(4) \(\sqrt{17}\)

Hint:

Solution:

(3) \(\sqrt{26}\)

Question 11.

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2 : 1 is

(1) \(\left(\frac{7}{2}, \frac{11}{2}\right)\)

(2) (3, 5)

(3) (4, 4)

(4) (4, 6)

Hint:

Question 12.

If P\(\left(\frac{a}{3}, \frac{b}{2}\right)\) is the mid-point of the line segment joining A(-4, 3) and B(-2, 4) then (a, b)

(1) (-9, 7)

(2) \(\left(-3, \frac{7}{2}\right)\)

(3) (9, -7)

(4) \(\left(3-\frac{7}{2}\right)\)

Hint:

Solution:

(1) (-9, 7)

Question 13.

In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(-2, 3)

(1) 1 : 2

(2) 2 : 1

(3) 1 : 3

(4) 3 : 1.

Hint:

Question 14.

If the coordinates of one end of a diameter of a circle is (3, 4) and the coordinates of its center is (-3, 2), then the coordinate of the other end of the diameter is

(1) (0, -3)

(2) (0, 9)

(3) (3, 0)

(4) (-9, 0)

Solution:

(4) (-9, 0)

Question 15.

The ratio in which the x-axis divides the line segment joining the points A(a_{1}, b_{1}) and B(a_{2}, b_{2}) is

(1) b_{1} : b_{2}

(2 ) -b_{1} : b_{2}

(3 ) a_{1} : a_{2}

(4 ) -a_{1} : a_{2}

Hint:

Solution:

(2 ) -b_{1} : b_{2}

Question 16.

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, -7) is

(1) 2 : 3

(2) 3 : 4

(3) 4 : 7

(4) 4 : 3

Hint:

Solution:

(3) 4 : 7

Question 17.

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, -3) respectively, then the vertices A and B of the triangle are

(1) (3, 2), (2, 4)

(2) (4, 0), (2, 8)

(3) (3, 4), (2, 0)

(4) (4, 3), (2, 4)

Hint:

0 + y_{2} = 8 ⇒ y_{2} = 8

(x_{1}, y_{1}) = (4, 0) ; (x_{2}, y_{2}) = (2, 8)

Solution:

(2) (4, 0), (2, 8)

Question 18.

The mid-point of the line joining (-a, 2b) and (-3a, -4b) is

(1) (2a, 3b)

(2) (-2a, -b)

(3) (2a, b)

(4) (-2a, -3b)

Hint:

Solution:

(2) (-2a, -b)

Question 19.

In what ratio does the j-axis divides the line joining the points (-5, 1) and (2, 3) internally

(1) 1 : 3

(2) 2 : 5

(3) 3 : 1

(4) 5 : 2

Hint:

Solution:

(4) 5 : 2

Question 20.

If (1, -2), (3, 6), (x, 10) and (3, 2) are the vertices of the parallelogram taken in order, then the value of x is

(1) 6

(2) 5

(3) 4

(4) 3

Hint:

In parallelogram diagonals bisect each other.

Mid point of AC = Mid point of BD

Solution:

(2) 5