Mathematics

What is the value of r if the distance between the point (4,2) and (1,r)…

What is the value of r if the distance between the point (4,2) and (1,r) is 3 units?
  • A.
    1
  • B.
    2
  • C.
    3
  • D.
    4
Correct Answer: Option B
Explanation

A(4,2) and B(1,r), AB = 3 units
3 = √ (x2– x1)2 + (y2-y1)2

3 = √ (4-1)2 + (2-r)2

3 = √ 32 + (2-r)2

3 = √ 9 + 4 – 4r + r2

3 = √ r2 – 4r + 13

9 = r2 – 4r + 13 By squaring both sides
r2 – 4r + 4 = 0
(r-2)(r-2) = 0
r = 2