233k views
15 votes

Which point is closer to the line y=1/2x+4, A(-2,6) or B (4,3)?

User Meisel
by
8.3k points

1 Answer

9 votes

9514 1404 393

Answer:

neither; they are the same distance from the line

Explanation:

The distance of point (x, y) from line ax+by+c=0 is given by ...

d = |ax +by +c|/(√a² +b²)

Since we're using the same line for both points, we only need to evaluate ...

d = |ax +by +c|

Subtracting y can put the equation in the desired form:

1/2x -y +4 = 0

__

For point A, the expression of interest evaluates to ...

|(1/2)(-2) -(6) +4| = |-1-6+4| = 3

For point B, the expression of interest evaluates to ...

|(1/2)(4) -(3) +4| = |2-3+4| = 3

These values tell us the points are the same distance from the line.

_____

The attached graph shows that circles of the same radius centered on A and B are both tangent to the line. Hence the distances are the same.

Which point is closer to the line y=1/2x+4, A(-2,6) or B (4,3)?-example-1
User Jason Striegel
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories