Question

find the value of k if the distance between the 2 points 1,4 and k,1 is 5​

Answer 1

Step-by-step explanation:

√(x2-x1)²+(y2-y1)²=5

(x2-x1)²+(y2-y1)²=25

(k-1)²+(1-4)²=25

k²+1-2k+9=25

k(k-2)=15

either K=15 or K=17

Answer 2

Answer:

k=2√5 units or points

Step-by-step explanation:

Let the two points be A and B

A=(1,4)=(x1,y1)

B=(k,1)=(x2,y2)

AB= 2 units

Using Distance formula ($\sqrt({x2} ^2-x1^2) + (y2^2-y1^2)$) (This is root of entire eqn)

AB=√(k^2-1)+(1^2-4^2)

=>2=√(k^2-1)-15   (Note: root is for whole eqn)

=>4=k^2-16   (Squaring both sides)

=>k^2=20

=>k=√20

=>k=2√5 units (or points whichever unit is mentioned)