If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is
(A) –2
(B) 2
(C) –1
(D) 1
Answers
Answer:
B . 2
it may helps you
thanks
Answer:
Option B
Step-by-step explanation:
Given :-
The distance between the points (2, –2) and
(–1, x) is 5.
To find :-
One of the values of x is
(A) –2
(B) 2
(C) –1
(D) 1
Solution :-
Given points are (2, –2) and (–1, x)
Let (x1, y1) = (2,-2) => x1 = 2 and y1 = -2
Let (x2, y2) = (-1,x) => x2 = -1 and y2 = x
We know that
The distance between the two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units
The distance between the given points
=> √[(-1-2)²+(x-(-2))²]
=> √[(-3)²+(x+2)²]
=> √[9+(x+2)²]
=> √(9+x²+4x+4)
=> √(x²+4x+13)
According to the given problem
The distance between the two points = 5
=> √(x²+4x+13) = 5
On squaring both sides then
=> [√(x²+4x+13) ]² = 5²
=> x²+4x+13 = 25
=> x²+4x+13-25 = 0
=> x²+4x-12 = 0
=> x²+6x-2x-12 = 0
=> x(x+6)-2(x+6) = 0
=> (x+6)(x-2) = 0
=> x+6 = 0 or x-2 = 0
=> x = -6 or x = 2
Therefore , the value of x is -6 or 2
Answer:-
The values of x -6 and 2
Used formulae:-
Distance formula:-
The distance between the two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units