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Find the distance from the point A(−2, 3) to the line y = 12x+1 . Round your answer to the nearest tenth.

User EMP
by
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1 Answer

2 votes

Answer:

2.2 to the nearest tenth.

Explanation:

The line y = 12x + 1

has a slope of 12 so the perpendicular line joining the point (-2, 3) to

y = 12x + 1 will have a slope of -1/12.

The equation of this line is

y - 3 = -1/12(x + 2)

that is:

y = -1/12x + 17/6

Equating the equations of the 2 lines will give us where they intersect:

12x + 1 = -1/12x + 17/6 Multiply through be 12:

144x + 12 = -x + 34

145x = 22

x = 22/145

= 0.1517

So y = 12(0.1517) + 1

= 2.8207.

So the distance between the points (0.1517, 2.8207) and (-2, 3)

= √[(3-2.8207)^2 + (-2-0.1517)^2]

= 2.1592

User Jordan Ell
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8.3k points