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chubhunter [2.5K]
3 years ago
14

How to find a point on a line in 3d given the distance from one of the points?

Mathematics
1 answer:
balu736 [363]3 years ago
7 0

Let a line in three dimensions be specified by two points  and  lying on it, so a vector along the line is given by

(1)The squared distance between a point on the line with parameter  and a point  is therefore(2)

To minimize the distance, set  and solve for  to obtain

(3)

where  denotes the dot product. The minimum distance can then be found by plugging  back into (2) to obtain

<span>(4)(5)</span>
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Answer:

1. y = 4x - 27

2. y = -4x - 15

Step-by-step explanation:

If two lines are parallel, then they have the same slope. So, the slope of the line we are looking for needs to be 4. We can start by writing a point-slope equation:

y - y1 = m(x - x1)

We can substitute the values we have, the point we are using is (8, 5) because it needs to be on the line:

y - 5 = 4(x - 8)

We can distribute:

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We are not given the slope-intercept form, so we must divide both sides by two to get it:

y = 1/4 x + 8

A perpendicular line has the slope that is the negative reciprocal of the one that is given. So, the slope of the line would be - 4. We can start by writing a point-slope equation:

y - y1 = m(x - x1)

We can substitute the values we have, the point we are using is (-5, 5) because it needs to be on the line:

y - 5 = -4(x + 5)

We can distribute:

y - 5 = -4x - 20

y = -4x - 15

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2x+8+ 120= 180
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2x+8+ 120= 180
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There is your answer :)
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