The value of K is 5 if (1,K) is equidistant from (4,0) and (-4, 8) after applying the distance formula.
It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
To find the value of K:
Distance between (1, K) to (4, 0) = Distance between (1, K) and (-4,8)
[tex]\rm \sqrt{(4-1)^2+(0-k)^2} = \rm \sqrt{(-4-1)^2+(8-K)^2}[/tex]
Squaring both side:
[tex]\rm {(4-1)^2+(0-k)^2} = \rm {(-4-1)^2+(8-K)^2}[/tex]
[tex]\rm 9+K^2=K^2-16K+89[/tex]
16K = 80
K = 5
Thus, the value of K is 5 if (1,K) is equidistant from (4,0) and (-4, 8) after applying the distance formula.
Learn more about the distance formula here:
brainly.com/question/18296211
#SPJ2
