Case Study Based Question on Coordinate Geoemtry
Republic Day Parade
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.
Based on the given information, answer the questions No. 41-45
1. If P is considered as origin, the coordinates of B are :
a) (8,5)
b) (3,8)
c) (8,0)
d) (0,3)
2. The distance between children standing at H and G is :
a) 8 units
b) 2 units
c) 5 units
d) √8 units
3. The coordinate of point which divides the line segment joining the points A and D in the ratio 2:3 internally are :
a) (6, 19/5)
b) (6,6)
c) (6,2)
d) (19/5, 6)
4. If a point (x,y) is equidistant from C(6,8) and F(6,1) then :
a) 2x-7y+36=0
b) 14y=63
c) x-y=5
d) x+y=5
5. If H is considered as origin, the coordinates of P are :
a) (2,3)
b) (-1,-3)
c) (-2,3)
d) (2,-3)
Doubt by Pushkar
Solution :
1. If P is considered as origin, the coordinates of B are :
a) (8,5)
b) (3,8)
c) (8,0)
d) (0,3)
Ans :
When P is considered as the origin then coordinates of B are (3,8)
Hence, b) (3,8) is the correct option.
2. The distance between children standing at H and G is :
a) 8 units
b) 2 units
c) 5 units
d) √8 units
Ans :
The coordinates of H and G are H(1,3) and G(3,1)
Using Distance Formula
HG = √(x2-x1)²+(y2-y1)²
= √(3-1)²+(1-3)²
= √(2)²+(-2)²
= √(4+4)
= √8 units
Hence, d) √8 units is the correct option.
3. The coordinate of point which divides the line segment joining the points A and D in the ratio 2:3 internally are :
a) (6, 19/5)
b) (6,6)
c) (6,2)
d) (19/5, 6)
Ans :
Coordinates of Point A and D are
A(1,6) D(8,6)
.___________.___________.
A(1,6) P(x,y) D(8,6)
(x1,y1) (x2,y2)
m1:m2 = 2:3
P(x,y) = [(m1x2+m2x1)/(m1+m2), (m1y2+m2y1)/(m1+m2)]
P(x,y) = [2(8)+3(1)/(2+3), 2(6)+3(6)/(2+3)]
P(x,y) = [(16+3)/5, (12+18)/5]
P(x,y) = [19/5, 30/5]
P(x,y) = [19/5,6]
Hence, d) (19/5, 6) would be the correct option.
4. If a point (x,y) is equidistant from C(6,8) and F(6,1) then:
a) 2x-7y+36=0
b) 14y=63
c) x-y=5
d) x+y=5
Ans :
Let P(x,y)
According to Question
PC = PF
Squaring both sides
PC²=PF²
(x-6)²+(y-8)²=(x-6)²+(y-1)²
[Using Distance Formula]
(y-8)²=(y-1)²
y²+64-16y=y²+1-2y
64-1=-2y+16y
63=14y
14y=63
Hence, b) 14y=63 would be the correct option.
5. If H is considered as origin, the coordinates of P are :
a) (2,3)
b) (-1,-3)
c) (-2,3)
d) (2,-3)
Ans :
When H is considered as the origin then coordinates of P are (-1,-3)
Hence, b) (-1,-3) would be the correct option.