9.5 The Distance from a Point to a Line in R2
Chapter
Chapter 9
Section
9.5
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Lectures 3 Videos
Solutions 27 Videos

Determine the distance from P(-4, 5) to each of the following lines:

3x + 4y - 5 = 0

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0.43mins
Q1a

Determine the distance from P(-4, 5) to each of the following lines:

5x -12y + 24 = 0

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0.43mins
Q1b

Determine the distance from P(-4, 5) to each of the following lines:

c) 9x - 40y = 0

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0.40mins
Q1c

Determine the distance between the following parallel lines:

a) 2x-y+1=0,2x-y+6=0

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1.15mins
Q2a

Determine the distance between the following parallel lines:

b) 7x - 24y + 168 =0, 7x - 24y - 336 = 0

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2.11mins
Q2b

Determine the distance from R(-2, 3) to each of the following lines:

a) \vec{r}=(-1,2)+s(3,4), s \in \mathbf{R}

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2.29mins
Q3a

Determine the distance from R(-2, 3) to each of the following lines:

b) \vec{r}=(1,0)+t(5,12), t \in \mathbf{R}

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1.29mins
Q3b

Determine the distance from R(-2, 3) to each of the following lines:

c) \vec{r} = (1, 3) + p(7, -24), p \in \mathbb{R}

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1.22mins
Q3c

Find the distance between the following lines:

a) The formula for the distance from a point to a line is d=\displaystyle{\frac{|Ax_0+by_0+C|}{\sqrt{A^2+B^2}}}. Show that this formula can be modified so the distance from the origin, O(0,0), to the line Ax+By+c=0 is given by the formula d=\displaystyle{\frac{|C|}{\sqrt{A^2+B^2}}}.

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0.35mins
Q4a

Find the distance between the following lines:

b) Determine the distance between L_1:3x-4y-12=0 and L_2:3x-4y+12=0 by first finding the distance from the origin to L_1 and then finding the distance from the origin to L_2.

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0.46mins
Q4b

Find the distance between the following lines:

b) Determine the distance between L_1:3x-4y-12=0 and L_2:3x-4y+12=0 by first finding the distance from the origin to L_1 and then finding the distance from the origin to L_2.

c) Find the distance between the two lines directly by first determining a point on one of the lines and then using the distance formula. How does this answer compare with the answer you found in part b.?

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0.57mins
Q4c

Calculate the distance between the following lines:

\vec{r}=(-2,1)+s(3,4):s \in \mathbb{R}:\vec{r}=(1,0)+t(3,4), t \in \mathbb{R}

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1.10mins
Q5a

Calculate the distance between the following lines:

b) \displaystyle{\frac{x-1}{4}}=\displaystyle{\frac{y}{-3}}, \displaystyle{\frac{x}{4}}=\displaystyle{\frac{y+1}{-3}}

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0.57mins
Q5b

Calculate the distance between the following lines:

c) 2x-3y+1=0,2x-3y-3=0

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0.46mins
Q5c

Calculate the distance between the following lines:

d) 5x+12y=120, 5x+12y+120=0

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0.41mins
Q5d

Calculate the distance between point P and the given line.

a) P(1,2,-1); \vec{r}=(1,0,0)+s(2,-1,2),s \in \mathbf{R}

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3.10mins
Q6a

Calculate the distance between point P and the given line.

b) P(0,-1,0); \vec{r}=(2,1,0)+t(-4,5,20), t \in \mathbf{R}

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1.37mins
Q6b

Calculate the distance between point P and the given line.

P(2,3,1); \vec{r}=p(12,-3,4), p \in \mathbf{R}

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1.33mins
Q6c

Calculate the distance between the following parallel lines.

a) \vec{r}=(1,1,0)+s(2,1,2),s \in \mathbf{R}; \vec{r}=(-1,1,2)+t(2,1,2), t \in \mathbf{R}

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1.56mins
Q7a

Calculate the distance between the following parallel lines.

\vec{r} = (3,1,-2) + m(1,1,3), m(1,1,3), m \in \mathbf{R}; \vec{r}=(1,0,1)+n(1,1,3), n \in \mathbf{R}

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1.34mins
Q7b

a) Determine the coordinates of the point on the line \vec{r}=(1,-1,2)+s(1,3,-1),s \in \mathbf{R}, that produces the shortest distance between the line and a point with coordinates (2,1,3).

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3.58mins
Q8a

a) Determine the coordinates of the point on the line \vec{r}=(1,-1,2)+s(1,3,-1),s \in \mathbf{R}, that produces the shortest distance between the line and a point with coordinates (2,1,3).

b) What is the distance between the given point and the line?

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1.05mins
Q8b

Two planes with equations x -y + 2z = 2 and x + y - z = -2 intersect along line L. Determine the distance from P(-1, 2, -1) to L, and determine the coordinates of the point on L that gives this minimal distance.

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5.47mins
Q9

The point A(2, 4, -5) is reflected in the line with equation \vec{r} = (0, 0, 1) + s(4, 2, 1), s \in \mathbb{R}, to give the point A'. Determine the coordinates of A'.

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5.45mins
Q10

A rectangular box with an open top, measuring 2 by 2 by 3, is constructed. Its vertices are labelled as shown.

Determine the distance from A to the line segment HB.

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1.36mins
Q11a

A rectangular box with an open top, measuring 2 by 2 by 3, is constructed. Its vertices are labelled as shown.

b) What other vertices on the box will give the same distance to HB as the distance you found in part a.?

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0.41mins
Q11b

A rectangular box with an open top, measuring 2 by 2 by 3, is constructed. Its vertices are labelled as shown.

c) Determine the area of the \triangle AHB.

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0.40mins
Q11c