Pls help solve the questions I need it before 7 pm I will give 100 points
Answers
Answer:
i) (2)
ii) (4)
iii) (2)
iv) (3)
Step-by-step explanation:
Given :-
The mid point of the line segment joining the points A(2,4) and B(x,y) is C(5,7) and C(5,7) is the mid point of the line segment joining the points E(a,b) and D(-3,-2).
To find :-
Find the following
See the above attachment
Solution :-
I) Given points are A(2,4) and B(x,y)
Let (x1, y1) = (2,4) => x1 = 2 and y1 = 4
Let (x2, y2) = (x,y) => x2 = x and y2 = y
The coordinates of the mid point of the like segment joining the points (x1, y1) and (x2, y2) is ((x1+x2)/2 , (y1+y2)/2)
The mid point of the line segment AB
= ( ( 2+x)/2 , (4+y)/2 )
According to the given problem
The mid point of AB = C(5,7)
=> ( ( 2+x)/2 , (4+y)/2 ) = (5,7)
On comparing both sides then
=> (2+x)/2 = 5 and (4+y)/2 = 7
=> 2+x = 5×2 and 4+y = 7×2
=> 2+x = 10 and 4+y = 14
=> x = 10-2 and y = 14-4
=> x = 8 and y = 10
Therefore, (x,y) = (8,10)
The coordinates of B = (8,10)
ii) given points are E(a,b) and D(-3,-2).
Let (x1, y1) = (a,b) => x1 = a and y1 = b
Let (x2, y2) = (-3,-2) => x2 = -3 and y2 = -2
The coordinates of the mid point of the like segment joining the points (x1, y1) and (x2, y2) is ((x1+x2)/2 , (y1+y2)/2)
The mid point of the line segment ED
= ( ( -3+a)/2 , (-2+b)/2 )
According to the given problem
The mid point of AB = C(5,7)
=> ( (-3+a)/2 , (-2+b)/2 ) = (5,7)
On comparing both sides then
=> (-3+a)/2 = 5 and (-2+b)/2 = 7
=> -3+a = 5×2 and -2+b = 7×2
=> -3+a= 10 and -2+b = 14
=> a = 10+3 and b = 14+2
=> a = 13 and b = 16
Therefore, (a,b) = (13,16)
The coordinates of E = (13,16)
iii) A = (2,4) and B = (8,10)
D = (-3,-2) and E = (13,16)
We know that
The distance between two points (x1, y1) and (x2 , y2) is √[(x2-x1)²+(y2-y1)²] units
Distance between A and E
Let (x1, y1) = (2,4) => x1 = 2 and y1 = 4
Let (x2, y2) = (13,16) => x2 = 13 and y2 = 16
=> AE = √[(13-2)²+(16-4)²]
=> AE = √(11²+12²)
=> AE= √(121+144)
=> AE = √265 units
and
Distance between B and E
Let (x1, y1) = (8,10) => x1 = 8 and y1 = 10
Let (x2, y2) = (13,16) => x2 = 13 and y2 = 16
=> BE = √[(13-8)²+(16-10)²]
=> BE = √(5²+6²)
=> BE = √(25+36)
=> BE = √61 units
and
Distance between B and D
Let (x1, y1) = (8,10) => x1 = 8 and y1 = 10
Let (x2, y2) = (-3,-2) => x2 = -3 and y2 = -2
=> BD = √[(-3-8)²+(-2-10)²]
=> BD = √((-11)²+(-12²)
=> BD = √(121+144)
=> BD = √265 units
and
Distance between A and D
Let (x1, y1) = (2,4) => x1 = 2 and y1 = 4
Let (x2, y2) = (-3,-2) => x2 = -3 and y2 = -2
=> AD = √[(-3-2)²+(-2-4)²]
=> AD = √((-5)²+(-6²))
=> AD = √(25+36)
=> AD = √61 units
We have ,
AE = BD and BE = AD
Two pair of opposite sides are equal
=> AEBD is a Parallelogram.
iv) Distance between A and B
Let (x1, y1) = (2,4) => x1 = 2 and y1 = 4
Let (x2, y2) = (8,10) => x2 = 8 and y2 = 10
=>AB = √[(8-2)²+(10-4)²]
=> AB = √(6²+6²)
=> AB = √(36+36)
=>AB = √72
=> AB = 6√2 units
Therefore, The length of AB = 6√2 units
Answer :-
I) The coordinates of B = (8,10)
ii) The coordinates of E = (13,16)
iii) AEBD is a Parallelogram.
iv) The length of AB = 6√2 units
Used formulae:-
→ Mid point formula:-
The coordinates of the mid point of the like segment joining the points (x1, y1) and (x2, y2) is ((x1+x2)/2 , (y1+y2)/2)
→ Distance formula:-
The distance between two points (x1, y1) and (x2 , y2) is √[(x2-x1)²+(y2-y1)²] units
Parallelogram:-
Two pairs of opposite sides are parallel and equal .
Answer:
a) 2
b) 3
c) 4
d) 1
hope it's helpful to you dear