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 = √ (x_{2}– x_{1})^{2} + (y_{2}-y_{1})^{2}
3 = √ (4-1)^{2} + (2-r)^{2}
3 = √ 3^{2} + (2-r)^{2}
3 = √ 9 + 4 – 4r + r^{2}
3 = √ r^{2} – 4r + 13
9 = r^{2} – 4r + 13 By squaring both sides
r^{2} – 4r + 4 = 0
(r-2)(r-2) = 0
r = 2