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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

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

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

Let P, Q be points of trisection of AB, with P closer to A and Q closer to B. Using your knowledge of how to find the coordinates of the midpoint of a segment, how would you find the coordinates of P and Q? Do this for the case when the points are A (4, 7) and B (16, –2).

P is one-third and Q is two-thirds along the segment. The total change in x is 12 and y is –9. Applying these shifts to A gives P (8, 4) and Q (12, 1).

Ayushree

Asked: April 26, 2026In: Class 9 Maths

Use the connection you found to find the coordinates of B given that M (–7, 1) is the midpoint of A (3, – 4) and B (x, y).

Use the midpoint formula: x-mid = (x1 + x2) / 2. For x: –7 = (3 + x) / 2 which gives x = –17. For y: 1 = (–4 + y) / 2 which gives y = 6. Point ...

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.

Let P, Q be points of trisection of AB, with P closer to A and Q closer to B. Using your knowledge of how to find the coordinates of the midpoint of a segment, how would you find the coordinates of P and Q? Do this for the case when the points are A (4, 7) and B (16, –2).

Use the connection you found to find the coordinates of B given that M (–7, 1) is the midpoint of A (3, – 4) and B (x, y).

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