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frozen [14]
3 years ago
8

Given point A(-4,3) and point B (-1,1), what is the distance in nearest feet between points A and B on this corporate campus?

Mathematics
1 answer:
laila [671]3 years ago
8 0

The closest distance is about 4 feet.

In order to find this, you can plot these two points. Once you have done so, you can create a right triangle in which the difference in x and the difference and y are the two legs. Then use the Pythagorean Theorem to find the hypotenuse (or distance between).

a^2 + b^2 = c^2

2^2 + 3^2 = c^2

4 + 9 = c^2

13 = c^2

Sqrt(13) = c = about 3.6

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Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.
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\frac{7}{\sqrt{3}}

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |                   --------------------(i)

From the question,

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d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |

d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |

d = |\frac{(-7)}{\sqrt{3}} |

d = \frac{7}{\sqrt{3}}

Therefore, the shortest distance from the point to the plane is  d = \frac{7}{\sqrt{3}}

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