Question

284%2C3%29%3F" id="TexFormula1" title="Which point is closer to the line y=1/2x+4, A(-2,6) or B (4,3)?" alt="Which point is closer to the line y=1/2x+4, A(-2,6) or B (4,3)?" align="absmiddle" class="latex-formula">

Answer 1

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Answer:

  neither; they are the same distance from the line

Step-by-step 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

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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.