Geometry Graphing - Find missing coordinate when given length of line segment

Question

Hello, I have been struggling with this particular question I feel like I know it I'm just fighting myself on which formula to use.

 

The questions state: Line segment AB is 2 to the square root of 10, where A has the coordinates (-3, 4) and B has coordiantes (-1, k) Find the value of K. 

 

so I found that AB is 6.32? I'm assuming it is rounded down to 6. 

 

Any help would be greatly appreciated. 

Answer 1

 

 

 

Hi Dennis

See if your answer matches ?

 

Length² =( X2 -X1 )² - (Y2 - Y1 )²

 

Length =  2 √10 given

Lenght ² = 4x10 = 40

 

40  = (- 1 +3)² + ( k-4)²

 

or k² - 8k -20 = 0

 

k² - 10 k +2 K -20 = 0

 

Gives k = -2 or 10