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Question
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.
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Solution
(i) The points is in the water. No, it is not in the same place as point A
(ii) No, they are not in the same place. The coordinates of points C and D are (7, 5) and (5, 7), respectively.
(iii) (2, 7) is in the water.
(iv) (7, 3), (5, 5)
(v) (8.5, 3)
(vi) (9, 4), (10, 4), (11, 5)
(vii) (5, 3), (6, 2), (7, 2)
Notes
Answer for option (vi) and (vii) may vary from student to student
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