Case Study Chapter 7 Coordinate Geometry Mathematics

l. Read the following and answer Shaurya made a map of his locality on a coordinate plane.   

Question. The coordinates of the point which divides the line segment joining school and park internally in the ratio 3 : 2 are   

(a) (–2, 2)
(b) (–2, –2)
(c) (2, 3)
(d) (2, –2)

Answer: A

Question. If he considered his house as the origin, then coordinates of market are   
(a) (3, –1)
(b) (–3, –1)
(c) (–3, 1)
(d) (3, 1)

Answer: B

Question. The distance of his friend Kartik’s house from his house is   
(a) √20 units
(b) √10 units
(c) 20 units
(d) 10 units

Answer: A

Question. If you form a polygon with vertex as position of park, Shaurya's home, railway station, post office and temple, then the polygon is   
(a) Regular polygon
(b) Convex Polygon
(c) Concave Polygon
(d) Rhombus

Answer: C

Question. There is a fort at a distance of 10 units from his house. If its ordinate is 6, then its abscissa is   
(a) ± 2
(b) 0
(c) ± 4
(d) ± 8

Answer: D

ll. Read the following and answer A coach is discussing the strategy of the game with his players. The position of players is marked with ‘×’ in the figure.   

Question. The player who is 6 units from x-axis and 2 units to the right of y-axis is at position     
(a) J
(b) B
(c) I
(d) A

Answer: A

Question. According to sudden requirement coach of the team decided to increase one player in the 4th quadrant without increasing the total number of players, so he decided to change the position of player F in such a way that F becomes symmetric to D w.r.t x axis, then new position of F is   
(a) (3, 4)
(b) (3, – 4)
(c) (–4, 3)
(d) (4, 3)

Answer: B

Question. If (x, y) are the coordinates of the mid-point of the line segment joining A and H, then     
(a) x = – 4, y = 2
(b) x = 2, y = 4
(c) x = –2, y = 4
(d) x = –4, y = – 2

Answer: A

Question. If O is taken as the origin, the point whose abscissa equal to zero is     
(a) H
(b) E
(c) G
(d) F

Answer: C

Question. The distance between the player C and B is     
(a) 5 units 
(b) 4 √2 units
(c) 2 √5 units
(d) 5 √2 units

Answer: B

lll. Read the following and answer The children of a school prepared a dance item for Republic Day parade for which they were asked to form a rectangle by standing at a fixed distance, taken as one unit. Some children, then formed a pattern inside the rectangle. 

Question. The coordinate of the point that divides the line segment joining the points A and D in the ratio 2 : 3 internally are     

(a) (6, 5 /19) 
(b) (6, 6)
(c) (6, 2)
(d) (19/5 , 6)

Answer: D

Question. The coordinates of the point P if H is taken as the origin are     
(a) (2, 3)
(b) (–1, –3)
(c) (–2, 3)
(d) (2, –3)

Answer: B

Question. If a point (x, y) is equidistant from C(6, 8) and F(6, 1) then     
(a) 2x – 7y + 36 = 0
(b) 144y = 63
(c) x – y = 5
(d) x + y = 5

Answer: B

Question. If P is considered as the origin, the coordinates of B are   
(a) (8, 5)
(b) (3, 8)
(c) (8, 0)
(d) (0, 3)

Answer: B

Question. The distance between the children standing at H and G is   
(a) 8 units  
(b) 2 units
(c) 5 units
(d) √8 units

Answer: D

lV. Read the following and answer The top of a table is shown in the figure given below: 

Question. The coordinates of the mid point of line segment joining points M and Q are   

(a) (9, 3)
(b) (5, 11)
(c) (14, 14)
(d) (7, 7)

Answer: D

Question. If G is taken as the origin, and x, y axis put along GF and GB, then the point denoted by coordinate (4, 2) is   
(a) H
(b) F
(c) Q
(d) R

Answer: C

Question. Which among the following have same ordinate ?   
(a) H and A
(b) T and O
(c) R and M
(d) N and R

Answer: B

Question. The coordinates of the points H and G are respectively   
(a) (1, 5), (5, 1)
(b) (0, 5), (5, 0)
(c) (1, 5), (5, 0)
(d) (5, 1), (1, 5)

Answer: A

Question. The distance between the points A and B is     
(a) 4 units
(b) 4 √2 units
(c) 16 units
(d) 32 units

Answer: B

V. Read the following and answer A rangoli design was made by Ishita using coordinate plane. 

Question. PQRS is a square inside the circle where P is (–1, 1) then coordinates of R are     

(a) (–1, –1)
(b) (–1, 1)
(c) (1, –1)
(d) (1, 1)

Answer: C

Question. The distance of the point M on the circle from x-axis is     
(a) 4 units
(b) 3 units
(c) 2 units
(d) 5 units

Answer: D

Question. The coordinates of the mid point of the line segment joining PR is     
(a) (1, 1)
(b) (0, 0)
(c) (–1, –1)
(d) (1, 2)

Answer: B

Question. If coordinates of centre X are (0, 0) and B is a point on circle with coordinates (7, 0), then coordinate of C and D are respectively   
(a) (0, 7), (0, – 7)
(b) (0, –7), (0, 7)
(c) (7, 7), (–7, – 7)
(d) (–7, –7), (7, 7)

Answer: A

Question. The coordinates of the point on the circle in first quadrant whose abscissa equal to 3 is   
(a) (3, 3) 
(b) (3, –3)
(c) (2√10, 3)
(d) (3, 2 √10)

Answer: D