class 9 maths ganita manjari chapter 1 pdf

Ayushree

Asked: April 26, 2026In: Class 9 Maths

Plot the points A (2, 1), B (–1, 2), C (–2, –1) and D (1, –2) in the coordinate plane. Is ABCD a square? Can you explain why? What is the area of this square?

Yes, it is a square. All four sides (AB, BC, CD, DA) equal the square root of 10. Both diagonals (AC and BD) equal the square root of 20. The total area is 10.

Ayushree

Asked: April 26, 2026In: Class 9 Maths

A computer graphics program displays images on a rectangular screen whose coordinate system has the origin at the bottom-left corner. The screen is 800 pixels wide and 600 pixels high. A circular icon of radius 80 pixels is drawn with its centre at the point A (100, 150). Another circular icon of radius 100 pixels is drawn with its centre at the point B (250, 230). Determine: (i) whether any part of either circle lies outside the screen. (ii) whether the two circles intersect each other.

(i) No part is outside. For A: 100 minus 80 is 20 (within 0 to 800). For B: 250 plus 100 is 350 (within 0 to 800). (ii) Distance between centers is 170. Sum of radii is 180. They intersect.

Ayushree

Asked: April 26, 2026In: Class 9 Maths

A city has two main roads which cross each other at the centre of the city. These two roads are along the North–South (N–S) direction and East–West (E–W) direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 10 streets in each direction. (i) Using 1 cm = 200 m, draw a model of the city in your notebook. Represent the roads/streets by single lines. (ii) There are street intersections in the model. Each street intersection is formed by two streets — one running in the N–S direction and another in the E–W direction. Each street intersection is referred to in the following manner: If the second street running in the N–S direction and 5th street in the E–W direction meet at some crossing, then we call this street intersection (2, 5). Using this convention, find: (a) how many street intersections can be referred to as (4, 3). (b) how many street intersections can be referred to as (3, 4).

(a) Only one unique intersection is referred to as (4, 3). (b) Only one unique intersection is referred to as (3, 4). In any coordinate system, every pair (x, y) represents exactly one specific point.

Ayushree

Asked: April 26, 2026In: Class 9 Maths

The midpoints of the sides of triangle ABC are the points D, E and F. Given that the coordinates of D, E and F are (5, 1), (6, 5) and (0, 3), respectively, find the coordinates of A, B and C.

Using vertex properties: A = E + F – D, giving (1, 7). B = D + F – E, giving (–1, –1). C = D + E – F, giving (11, 3). These coordinates form the original triangle ABC.

Ayushree

Asked: April 26, 2026In: Class 9 Maths

(i) Given the points A (1, – 8), B (– 4, 7) and C (–7, – 4), show that they lie on a circle K whose center is the origin O (0, 0). What is the radius of circle K? (ii) Given the points D (–5, 6) and E (0, 9), check whether D and E lie within the circle, on the circle or outside the circle K.

Radius squared is 1 squared plus –8 squared, which is 65. For D: (–5) squared plus 6 squared is 61. Since 61 is less than 65, D is inside. For E: 0 squared plus 9 squared is 81. E is ...

Plot the points A (2, 1), B (–1, 2), C (–2, –1) and D (1, –2) in the coordinate plane. Is ABCD a square? Can you explain why? What is the area of this square?

The midpoints of the sides of triangle ABC are the points D, E and F. Given that the coordinates of D, E and F are (5, 1), (6, 5) and (0, 3), respectively, find the coordinates of A, B and C.

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