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# This graph shows a map of an island just off the coast of a continent. The point labelled B represents a major city on the coast. The distance between grid lines represents 1 km.

Point A represents a resort that is located 5 km East and 3 km North of Point B. The values 5 and 3 are the coordinates of Point A. The coordinates can be given as the ordered pair (5, 3), where 5 is the horizontal coordinate and 3 is the vertical coordinate.

(i) On a copy of the map, mark the point that is 3 km East and 5 km North of Point B and label it S. Is Point S in the water or on the island? Is Point S in the same place as Point A?

(ii) Mark the point that is 7 km east and 5 km north of Point B and label it C. Then mark the point that is 5 km east and 7 km north of Point B and label it D. Are Points C and D in the same place? Give the coordinates of Points C and D.

(iii) Which point is in the water, (2, 7) or (7, 2)? Mark the point which is in water on your map and label it E.

(iv) Give the coordinates of two points on the island that are exactly 2 km from Point A.

(v) Give the coordinates of the point that is halfway between Points L and P.

(vi) List three points on the island with their x-coordinates greater than 8.

(vii) List three points on the island with a y-coordinate less than 4.

**Solution:**

(i) The graph below shows the point ‘S’ on the map which has the coordinates (5,3) and it lies In the sea. And it is not the same point as A.

(ii) The point C is 7 km east and 5 km north of point B and is marked as C. The point D is 5 km east and 7 Km north of point B and is marked as D. They are both shown on the map below. C and D are not the same place. The coordinates of C are (7, 5) and the coordinates of D are (5, 7).

(iii) Point (2,7) is in the sea and is marked as E.

(iv) The coordinates of the two points that are exactly 2 km away from A are P(7, 3) and F(5,5). There can be other points too.

(v) Coordinates of the point halfway between L and P is M(8, 3)

(vi) Three points on the island that have x greater than 8 can be (9,2), (10, 2) and (9,3). There can be more points with x greater than 8.

(vii) Three points on the island with y-coordinate less than 4 can be A (5, 3), P(7,3) and L(9,3). There can be other points like (8, 3) or (9,3) etc.

Please Note:

In the NCERT solutions for this exercise i.e. Unit 12

- The answer to point (iv) is written as (6, 11) whereas the question is asking for coordinates of two points which are 2 km from point A.
- The answer to the part (v) is given as two points (7,30 and (5,5) whereas the question is asking for the midpoint coordinates i.e. the midpoint between L and P
- Similarly the answer to the part (iv) in the NCERT solution is given as (6, 11) whereas the question is asking for coordinates of two points which are 2 Km from A.
- Answer to part vi is given as one point (7.5, 3) 2 km. The question is asking for three points.that have x greater than 8
- The answer to part (vii) is also given as one point whereas the question is asking for three points with y-coordinate less than 4.
- There is no part (viii) but the ncert solution has given answer to part (viii) as (6.25, 3)
- It seems that points P and L in the original diagram in the NCERT are not marked properly. Hence the points P and L have been marked again on the grid/graph.

**✦ Try This: **This graph shows a group of Islands just off the coast of a continent. The point labelled B represents a major city on the coast. The islands are labelled as I1, I2, I3, I4, and I5. The distance between grid lines represents 1 km.

(i) Which is the point which is closest to city B located on the coast of the continent? Give its coordinates.

(ii) Which other point on island I1 is exactly north of point L? What are its coordinates and its distance from point L?

(iii) Which are points on island I2 and what are their coordinates?

(iv) How far is Point C (island I2) from point M(Island I1)?

(v) Which three points have the same y coordinate?

(vi) The northernmost point is on which Island?

(vii) Which point on Island I2 is located exactly north of point A located on island I5?

(viii) Which is the easternmost point on the graph?

(i)The closest point to city B off the coast will be L (on Island I1) the coordinates of

which will be (2,3).

(ii)The point on island I1 which is exactly north of L is M. The coordinates of which are (2,7) and it is 5 km north of L

(iii)The points on island I2 are C and D. The coordinates of C and D are (5,8) and (9,7) respectively.

(iv)Point C on island I2 is 3 km from point M on Island I1.

(v)The points A(Island I5), P(Island I4) and L(Island I1) have the same y coordinate y = 3.

(vi) The northernmost point is on Island I2

(vii)The point located exactly north of point A is point C

(viii) The easternmost point is E.

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 15

**NCERT Exemplar Class 8 Maths Chapter 12 Problem 80**

## This graph shows a map of an island just off the coast of a continent. The point labelled B represents a major city on the coast. The distance between grid lines represents 1 km.

**Summary:**

The grid map shows the various points on the mainland, the sea and the island. It helps identify coordinates and distance of the points from the origin

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