Question

The distance wetween the points (2 ,k) and (-4, 1) is 2sqrt(10) units then the value of k is (A) -3 B) -1 c) 1 (a) None if these.​

Answer 1

Solution

Given :-

• The distance wetween the points (2 ,k) and (-4, 1) is 2√10.

Find :-

• Value of k

Explanation

Let,

P (x,y) & Q(x',y') be any two point of any surface .

Then, If we calculate Distance between both point , it will be

$\boxed{\tt{\red{\:(DistancePQ)\:=\:\sqrt{(x-x')^2+(y-y')^2}}}}$

Let, in this question

point be A(2,k) & B(-4,1) .

Here,

• x = 2
• y = k
• x' = -4
• y = 1

Now, keep all values in this Equation,

==> Distance (AB) = √[(2+4)² + (k-1)²]

==>Distance AB = √[(6)² + (k-1)²]

==> 2√10 = √[(36 + (k-1)²]________(1)

Squaring both side of equ(1)

==> (2√10)² = [√36 + (k-1)²]²

==> 2√10 × 2√10 = 36 + (k-1)²

==> 4×10 = 36 + k² +1 - 2k

==> 40 - 36 - 1 = k² - 2k

==> k² - 2k = 3

==> k² - 2k - 3 = 0

==> k² - 3k + k - 3 = 0

==> k(k-3) + 1(k-3) = 0

==> (k-3)(k+1) = 0

==> (k+1) = 0 Or, (k-3) = 0

==> k = -1 Or, k = 3

Hence

• Value of k will be = -1 Or, 3

_____________________

Answer 2

Answer:

-1 or 3

Step-by-step explanation:

according to distance formula