Exercise 5.6 - Chapter 5 Coordinate Geometry 9th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

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
 

Quéstión $2 .$
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 ${ }^{\text {nd }}$ quadrant and $(+,-)$ lies in IV th quadrant
Solution:
(3) II and IV quadrant respectively
 

Question $3 .$
On plotting the points $0(0,0), \mathrm{A}(3,-4), \mathrm{B}(3,4)$ and $\mathrm{C}(0,4)$ and joining $\mathrm{OA}, \mathrm{AB}, \mathrm{BC}$ and $\mathrm{CO}$, 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) $\mathrm{P}$ and $\mathrm{T}$
(2) $\mathrm{Q}$ and $\mathrm{R}$
(3) only $S$
(4) $\mathrm{P}$ and $\mathrm{Q}$
Hint: Points in IVth quadrant are $(+,-)$
Solution:
(2) $\mathrm{Q}$ and $\mathrm{R}$
 

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 $\mathrm{A}(2,0), \mathrm{B}(-6,0), \mathrm{C}(3, \mathrm{a}-3)$ lie on the $\mathrm{x}$-axis then the value of $\mathrm{a}$ is
(1) 0
(2) 2
(3) 3
(4) $-6$
Hint: Points in $y$-axis have ordinate zero. $\therefore \mathrm{a}-3=0 \Rightarrow \mathrm{a}=3$
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: $x+2=5 \Rightarrow x=3 ; y-2=4 \Rightarrow y=6$
Solution:
(3) $(3,6)$

Question $9 .$
If $Q_{1}, Q_{2}, Q_{3}, Q_{4}$ are the quadrants in a Cartesian plane then $Q_{2} \cap Q_{3}$ is
(1) $\mathrm{Q}_{1} \cup \mathrm{Q}_{2}$
(2) $\mathrm{Q}_{2} \cup \mathrm{Q}_{3}$
(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:
Distance $=\sqrt{(5-0)^{2}(-1-0)^{2}}=\sqrt{5^{2}+1^{2}}=\sqrt{26}$
Solution:
(3) $\sqrt{26}$

Question 11.
The coordinates of the point $\mathrm{C}$ dividing the line segment joining the points $\mathrm{P}(2,4)$ and $\mathrm{Q}(5,7)$ internally in the ratio $2: 1$ is
(1) $\left(\frac{7}{2}, \frac{11}{2}\right)$
(2) $(3,5)$
(3) $(4,4)$
(4) $(4,6)$

Solution:

(4) $(4,6)$

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

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) $3: 1$.

Solution:

1:3

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 $\mathrm{x}$-axis divides the line segment joining the points $\mathrm{A}\left(\mathrm{a}_{1}, \mathrm{~b}_{1}\right)$ and $\mathrm{B}\left(\mathrm{a}_{2}, \mathrm{~b}_{2}\right)$ is
(1) $b_{1}: b_{2}$
(2) $-b_{1}: b_{2}$
(3) $a_{1}: a_{2}$
(4) $-a_{1}: a_{2}$

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) $4: 3$

Solution:
(3) $4: 7$

Question $17 .$
If the coordinates of the mid-points of the sides $\mathrm{AB}, \mathrm{BC}$ and $\mathrm{CA}$ 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) $(4,3),(2,4)$

Solution:
(2) $(4,0),(2,8)$

Question $18 .$
The mid-point of the line joining $(-a, 2 b)$ and $(-3 a,-4 b)$ is
(1) $(2 a, 3 b)$
(2) $(-2 a,-b)$
(3) $(2 a, b)$
(4) $(-2 a,-3 b)$

Solution:
(2) $(-2 a,-b)$

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) $7.5$
(3) $3: 1$
(4) $5: 2$

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

Solution

(2) 5