9th Standard Syllabus & Materials
9th Standard
TN 9th Tamil உள்ளத்தின் சீர் -கற்கண்டு (இலக்கணம்) - தொடர் இலக்கணம், ஆகுபெயர் Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil உள்ளத்தின் சீர் -விரிவானம் (துணைப்பாடம்) - தாய்மைக்கு வறட்சி இல்லை! Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil உள்ளத்தின் சீர் -கவிதை பேழை (செய்யுள்) - மார்கழி பெருவிழா Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil உயிருக்கு வேர்-இலக்கணம் - பகுபத உறுப்பிலக்கணம் Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil அமுதென்று பேர் - இலக்கணம்-எழுத்து -அளபெடை Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil அமுதென்று பேர்-துணைப்பாடம் - ஆறாம்திணை Important Questions And Answers Study Material - QB365 Set A
Published on: 31/08/2026
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.
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Take MCQ Maths Test
1.
If \(\left( \frac { 3 }{ 2 } ,5 \right) ,\left( 7,\frac { -9 }{ 2 } \right) \)and\((\frac{13}{2},\frac{-13}{2})\) are mid-points of the sides of a triangle, then find the centroid of the triangle.
2.
ABC is a triangle whose vertices are A(3, 4), B(−2, −1) and C(5, 3) . If G is the centroid and BDCG is a parallelogram then find the coordinates of the vertex D.
3.
The vertices of a triangle are (1, 2), (h, −3) and (−4, k). If the centroid of the triangle is at the point (5, −1) then find the value of \(\sqrt { { (h+k) }^{ 2 }+{ (h+3k) }^{ 2 } } \)
4.
Find the length of median through A of a triangle whose vertices are A(−1, 3), B(1, −1) and C(5, 1).
5.
If the centroid of a triangle is at (4, −2) and two of its vertices are (3, −2) and (5, 2) then find the third vertex of the triangle.
6.
Using section formula, show that the points A(7, −5), B(9, −3) and C(13, 1) are collinear.
7.
In what ratio does the point P(2, −5) divide the line segment joining A(−3, 5) and B(4, −9) .
8.
Find the coordinates of the point which divides the line segment joining the points A(4,−3) and B(9,7) in the ratio 3:2.
9.
P divides AB in the ratio m: n. If P is the midpoint of AB then m : n = __________
1:1
2:1
1:2
none of these
10.
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 ______.
6
5
4
3
11.
In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally ______.
1 :3
2 :5
3 :1
5 :2
12.
The mid-point of the line joining (−a, 2b) and (−3a,−4b) is ______.
(2a, 3b)
(−2a, −b)
(2a, b)
(−2a, −3b)
13.
The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is ______.
2:3
3:4
4:7
4:3
1.
"The centroid of the triangle obtained by joining the mid points of the sides of a triangle is the same as the centroid of the original triangle."
\(\therefore\) The mid points of the sides of the triangle are given as
x1y1 , x2y, x3y3
\(\left( \frac { 3 }{ 2 } ,5 \right) \left( 7,\frac { -9 }{ 2 } \right) \left( \frac { 13 }{ 2 } ,\frac { -13 }{ 2 } \right) \)
\(\therefore\)Centroid \(=\left( \frac { { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 } }{ 3 } ,\frac { { y }_{ 1 }+{ y }_{ 2 }+{ y }_{ 3 } }{ 3 } \right) \)
\(=\left( \frac { \frac { 3 }{ 2 } +\frac { 7 }{ 1 } +\frac { 13 }{ 2 } }{ 3 } ,\frac { 5+\left( \frac { -9 }{ 2 } \right) +\frac { (-13) }{ 2 } }{ 3 } \right) =\left( \frac { \frac { 3+14+13 }{ 2 } }{ 3 } ,\frac { \frac { 10-9-13 }{ 2 } }{ 3 } \right) \)
\(=\left( \frac { \frac { 30 }{ 2 } }{ 3 } ,\frac { \frac { -12 }{ 2 } }{ 3 } \right) =\left( \frac { 15 }{ 3 } ,\frac { -6 }{ 3 } \right) =(5,-2)\)
2.
Centroid G =\(\left( \frac { { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 } }{ 3 } ,\frac { { y }_{ 1 }+{ y }_{ 2 }+{ y }_{ 3 } }{ 3 } \right) \)
\(\therefore G(x,y)=\left( \frac { 3+(-2)+5 }{ 3 } ,\frac { 4+(-1)+3 }{ 3 } \right) \)
\(=\left( \frac { 8-2 }{ 3 } ,\frac { 7-1 }{ 3 } \right) =\left( \frac { 6 }{ 3 } ,\frac { 6 }{ 3 } \right) =(2,2)\)
In a parallelogram diagonals bisect each other
∴ Mid point of DG = Mid point of BC
\(\left( \frac { x+2 }{ 2 } ,\frac { y+2 }{ 2 } \right) =\left( \frac { -2+5 }{ 2 } ,\frac { -1+3 }{ 2 } \right) \)
\(\frac { x+2 }{ 2 } =\frac { 3 }{ 2 } \)
x+2 = 3
x = 3 - 2 = 1
\(\frac { y+2 }{ 2 } =\frac { 2 }{ 2 } \)
y = 2 - 2 = 0
y + 2 = 2
\(\therefore\) The co-ordinates of the vertex D (x, y) = (1, 0)
3.
Vertices of a triangle
(x1 ,y1) = (1,2)
(x2,y2) = (h,-3)
(x3, y3) = (-4, k)
Centroid G (x,y) = (5, -1)
\(G=\left( \frac { { x }_{ 1 }+{ x }_{ 2 }+{ x }_{ 3 } }{ 3 } ,\frac { { y }_{ 1 }+{ y }_{ 2 }+{ y }_{ 3 } }{ 3 } \right) =(5,-1)\)
\(\left( \frac { 1+h+(-4) }{ 3 } ,\frac { 2+(-3)+k }{ 3 } \right) =(5,-1)\)
\(\Rightarrow \frac { -3+h }{ 3 } =5\)
-3 + h = 15
h = 18
\(\frac { 2-3+k }{ 3 } =-1\)
\(\therefore \sqrt { { (h+k) }^{ 2 }+{ (h+3k) }^{ 2 } } \)
\(=\sqrt { (18+(-2))^{ 2 }+{ (18+3(-2)) }^{ 2 } } \)
\(=\sqrt { { 16 }^{ 2 }+{ 12 }^{ 2 } } =\sqrt { 256+144 } =\sqrt { 400 } =20\)
4.
D (x, y) is the Mid point BC
\(\therefore \ D(x,y)=\left( \frac { 1+5 }{ 2 } ,\frac { -1+1 }{ 2 } \right) \)
\(=\left( \frac { 6 }{ 2 } ,\frac { 0 }{ 2 } \right) \)
= (3, 0)
AD is the median through A
Here A x2 y2 D x3 y3
(-1,3) (3,0)
\( \therefore\) Length of AD \(=\sqrt { { ({ x }_{ 2 }-{ x }_{ 1 }) }^{ 2 }+{ ({ y }_{ 2 }-{ y }_{ 1 }) }^{ 2 } } =\sqrt { { (3-(-1)) }^{ 2 }+{ (0-3) }^{ 2 } } \)
\(=\sqrt { { (3+1) }^{ 2 }+{ (-3) }^{ 2 } } =\sqrt { 16+9 } =\sqrt { 25 } =5\) units
5.
Centroid G (x,y) = (4, -2)
two vertices (x1, y1) = (3, -2)
(x2, y2) = (5, 2), (x3, y3) =?
\(\frac { 8+{ x }_{ 3 } }{ 3 } =4\ \ \frac { { y }_{ 3 } }{ 3 } =-2\)
8 + x3 = 12 y3 = -6
x3 = 4
∴ The third vertex (x3, y3) = (4, -6)
6.
x1 y1 x2 y2
A(7, -5) B(9, -3)
\(\bar { AB } =\sqrt { { ({ x }_{ 2 }-{ x }_{ 1 }) }^{ 2 }+{ ({ y }_{ 2 }-{ y }_{ 1 }) }^{ 2 } } \)
\(=\sqrt { { (9-7) }^{ 2 }+{ (-3-(-5)) }^{ 2 } } =\sqrt { { 2 }^{ 2 }+{ (-3+5) }^{ 2 } } =\sqrt { 4+4 } \)
\(=\sqrt { 8 } =\sqrt { 4\times 2 } =2\sqrt { 2 } \)
\(\bar { BC } =\sqrt { { (13-7 })^{ 2 }+{ (1-(-5)) }^{ 2 } } =\sqrt { { 4 }^{ 2 }+{ 4 }^{ 2 } } =\sqrt { 16+16 } \)
\(=\sqrt { 32 } =\sqrt { 16\times 2 } =4\sqrt { 2 } \)
\(\bar { AC } =\sqrt { { (13-7) }^{ 2 }+{ (1-(-5)) }^{ 2 } } \)
\(=\sqrt { { 6 }^{ 2 }+{ 6 }^{ 2 } } =\sqrt { 36+36 } \)
\(=\sqrt { { 6 }^{ 2 }+{ 6 }^{ 2 } } =\sqrt { 36+36 } \)
\(2\sqrt { 2 } +4\sqrt { 2 } =6\sqrt { 2 } \)
∴ AB + BC = AC, Here B is the common Point
∴ A, B, C are collinear
7.
x1 y1 x2 y2
A(-3, 5) B(4, -9) P(2, -5)
\(=P(x,y)\left( \frac { { mx }_{ 2 }+{ nx }_{ 1 } }{ m+n } ,\frac { { my }_{ 2 }+{ ny }_{ 1 } }{ m+n } \right) \)
\(P(2,-5)=\left( \frac { m\times 4+n(-5) }{ m+n } ,\frac { m\times (-9)+n(5) }{ m+n } \right) \)
\(\left( \frac { 4m-3n }{ m+n } \right) =2\)
4m -3n = 2m+ 2n
4m -2m = 2n + 3n
2m = 5n
\(\frac { m }{ n } =\frac { 5 }{ 2 } \)
∴ The ratio m : n = 5 : 2
8.
x1 y1 x2 y2 m : n
A (4, -3), B (9, 7), 3 : 2
By section formula \(P\left( \frac { { mx }_{ 2 }+{ nx }_{ 1 } }{ m+n } ,\frac { { my }_{ 2 }+{ ny }_{ 1 } }{ m+n } \right) =P(x,y) \)
\(P(x,y)=\left( \frac { 3(9)+2(4) }{ 3+2 } ,\frac { 3(7)+2(-3) }{ 3+2 } \right) \)
\(=\left( \frac { 27+8 }{ 5 } ,\frac { 21-6 }{ 5 } \right) =\left( \frac { 35 }{ 5 } ,\frac { 15 }{ 5 } \right) =(7,3)\)
9.
(a)
1:1
10.
(b)
5
11.
(d)
5 :2
12.
(b)
(−2a, −b)
13.
(c)
4:7
9th Standard Syllabus & Materials
9th Standard
TN 9th Tamil உள்ளத்தின் சீர் - திருக்குறள் Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil உள்ளத்தின் சீர் - மணிமேகலை Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil உள்ளத்தின் சீர் - ஏறு தழுவுதல் Important Questions And Answers Study Material - QB365 Set A
NEW9th Standard
TN 9th Tamil உயிருக்கு வேர் - தண்ணீர் Important Questions And Answers Study Material - QB365 Set A
Tamilnadu Stateboard 9th Standard Subjects
Tamilnadu Stateboard Standards
