Question

Find the value of K so that the distance between A(K,-4) and B(-2,K) is 10​

Answer 1

Given :

Two points A(K,-4) and B(-2,K)

Distance between two points A and B is 10 units

To Find :

Value of K

Solution :

AB = 10 units

AB² = 100 units

Using Distance formula we get

( -2 -k )² + ( k + 4 )² = 100

4 + k² + 4k + k² + 16 + 8k = 100

2k² + 12k = 80

k² + 6k = 40

k² + 10k - 4k - 40 = 0

k( k + 10) -4(k + 10) = 0

( k + 10)( k - 4 ) = 0

k = -10 , k = 4

Thus -10 and 4 are required values of k.

Answer 2

Step-by-step explanation:

✏️ QUESTIONS ✏️

Find the value of K so that the distance between A(K,-4) and B(-2,K) is 10?

✏️ANSWER✏️

Given points A(X1,X2)=(k,-4)

=>X1=k , y1=-4

B(X2,y2)=(-2,k)

=>X2 =-2 , y2 =k

Distance of AB =10 units

WKT:

The distance between A(x1,y1) B(X2,y2) is

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

$\sqrt{ {( - 2 - k)}^{2} + {(k - (4))}^{2} } = 10$

$= > \sqrt{ {( - 2 - k)}^{2} + {(k + 4)}^{2} } = 10$

squaring on both sides,

(-2-k)²+(k+4)²=100

4+k²+4k+k²+16+8k=100

2k²+12k+20=100

k²+6k+10=50

k²+6k-40=0

Splitting middle term:

k²-4k+10k-40=0

k(k-4)+10(k-4)=0

(k+10)(k-4)=0

k=-10

k=4