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Published on: 03/09/2019
Coordinate Geometry
Download Tamil Nadu 9th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
In which quadrant does the following points lie? (–7, 3)
2.
In which quadrant does the following points lie? (2, 5)
3.
In which quadrant does the following points lie? (3,–8)
4.
Show that the following points taken in order form an isosceles triangle A (6, –4), B (–2, –4), C (2, 10)
5.
Determine whether the given set of points in each case are collinear or not (–2, –8), (2, –3) (6, 2)
6.
Find the distance between the points (–4, 3), (2, –3).
7.
Show that (4, 3) is the centre of the circle passing through the points (9, 3), (7, –1), (–1, 3). Find the radius.
8.
Plot the following points A(2, 2), B(–2, 2), C(–2, –1), D(2, –1) in the Cartesian plane. Discuss the type of the diagram by joining all the points taken in order
9.
The point whose ordinate is 4 and which lies on the y-axis is ______.
( 4, 0 )
(0, 4)
(1, 4)
(4, 2)
10.
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 ______.
P and T
Q and R
only S
P and Q
11.
On plotting the points O(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?
Square
Rectangle
Trapezium
Rhombus
12.
The point M lies in the IV quadrant. The coordinates of M is _______
(a,b)
(–a, b)
(a, –b)
(–a, –b)
13.
Point (–3, 5) lie in the ________ quadrant
I
II
III
IV
1.
The x-coordinate is negative and y – coordinate is positive. So, Point(–7,3) lies in the II quadrant
2.
The x-coordinate is positive and y – coordinate is positive. So Point (2,5) lies in the I quadrant
3.
The x- coordinate is positive and y – coordinate is negative. So, Point(3,–8) lies in the IV quadrant.
4.
Distance = \(\sqrt { ({ x }_{ 2 }-{ x }_{ 1 })^{ 2 }+({ y }_{ 2 }-y_{ 1 })^{ 2 } } \)
AB= \(\sqrt { (-2-6)^{ 2 }+(-4+4)^{ 2 } } \)
= \(\sqrt { (-8)^{ 2 }+0 } =\sqrt { 64 } =8\)
BC = \(\sqrt { (2+2)^{ 2 }+(10+4)^{ 2 } } \)
= \(\sqrt { (4)^{ 2 }+(14)^{ 2 } } =\sqrt { 16+196 } =\sqrt { 212 } \)
AC = \(\sqrt { (2-6)^{ 2 }+(10+4)^{ 2 } } \)
= \(\sqrt { (-4)^{ 2 }+(14)^{ 2 } } =\sqrt { 1+-196 } =\sqrt { 212 } \)
BC = AC =\(\sqrt { 212 } \) (Two sides are equal)
∴ ABC is an isosceles triangle.
5.
Distance AB =\(\sqrt { (2+2)^{ 2 }+(-3+8)^{ 2 } } \)
= \(\sqrt { (4)^{ 2 }+(5)^{ 2 } } =\sqrt { 16+25 } =\sqrt { 41 } \)
BC =\(\sqrt { (6-2)^{ 2 }+(2+3)^{ 2 } } \)
= \(\sqrt { (4)^{ 2 }+(5)^{ 2 } } =\sqrt { 16+25 } =\sqrt { 41 } \)
AC = \(\sqrt { (6+2)^{ 2 }+(2+8)^{ 2 } } \)
= \(\sqrt { (8)^{ 2 }+(10)^{ 2 } } =\sqrt { 64+100 } =\sqrt { 164 } \)
= \(\sqrt { 4\times 41 } =2\sqrt { 41 } \)
AB + BC = AC ⇒ \(\sqrt { 41 } +\sqrt { 41 } =2\sqrt { 41 } \)
∴ The given three points are collinear.
6.
The distance between the points (-4, 3), (2, -3) is
\(d=\sqrt { \left( { x }_{ 2 }-{ x }_{ 1 } \right) ^{ 2 }+\left( y_{ 2 }-y_{ 1 } \right) ^{ 2 } } \)
\(=\sqrt { \left( 2+4 \right) ^{ 2 }+\left( -3-3 \right) ^{ 2 } } \)
\(=\sqrt { \left( { 6 }^{ 2 }+\left( -6 \right) ^{ 2 } \right) } =\sqrt { \left( 36+36 \right) } \)
\(=\sqrt { 36\times 2 } \)
\(=6\sqrt { 2 } \)
7.
Let P(4, 3), A(9, 3), B(7, –1) and C(–1, 3)
If P is the centre of the circle which passes through the points A, B, and C, then P is equidistant from A, B and C (i.e.) PA = PB = PC
By distance formula,
\(d=\sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2}\)
\(AP=PA =\sqrt{(4-9)^2+(3-3)^2}=\sqrt{(-5)^2+0}=\sqrt{25}=5\)
\(BP=PB =\sqrt{(4-7)^2+(3+1)^2}=\sqrt{(3)^2+(4)^2}=\sqrt{9+16}=\sqrt{25}=5\)
\(CP=CB =\sqrt{(4+1)^2+(3-3)^2}=\sqrt{(5)^2+0}=\sqrt{25}=5\)
PA = PB = PC, Radius = 5
Therefore P is the centre of the circle, passing through A, B and C
8.
| Point | A | B | C | D |
| Quadrant | I | II | III | IV |
Can you find the length, breadth and area of the rectangle?
ABCD is a rectangle.
9.
(b)
(0, 4)
10.
(b)
Q and R
11.
(c)
Trapezium
12.
(c)
(a, –b)
13.
(b)
II
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Tamilnadu Stateboard 9th Standard Subjects
Tamilnadu Stateboard Standards
