What is the value of r if the distance between the point (4,2) and (1,r) is 3 units?
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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
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