# arrow_back What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?

213 views
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?

In $R^{2}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ is $$D=\frac{\left|a x_{0}+b y_{0}+c\right|}{\sqrt{a^{2}+b^{2}}}$$
by Platinum
(119,140 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
1 answer 58 views
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is
1 answer 222 views
Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ isProve that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is $$D=\frac{\left| ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. 1 answer 55 views Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1.Find the distance D between the point (1,-4,-3) and the plane 2 x-3 y+6 z=-1. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal to 0 answers 58 views The distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal toThe distance from the point (1,1,1) to the plane  2 x-10 y+11 z-4=0  is equal to &nbsp; A) \dfrac{1}{3} B) 3 C) \dfrac{1}{15} D) 5 E) no ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain. 0 answers 157 views Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain.Do the points A(1,1,1), B(-2,0,3), and C(-3,-1,1) form the vertices of a right triangle? Explain. ... close 0 answers 297 views Let \mathbf{r}_{0}=\left(x_{0}, y_{0}\right) be a fixed vector in R^{2}. In each part, describe in words the set of all vectors \mathbf{r}=(x, y) that satisfy the stated condition.Let \mathbf{r}_{0}=\left(x_{0}, y_{0}\right) be a fixed vector in R^{2}. In each part, describe in words the set of all vectors \mathbf{r}=(x, y) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The distance from the point (-1,1,1) to the plane 0 answers 43 views The distance from the point (-1,1,1) to the planeThe distance from the point (-1,1,1) to the plane$$ 2 x-10 y+11 z-4=0 $$is equal to &nbsp; A) 3 B) \frac{1}{3} C) 5 D) \frac{1}{5} E) no ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine whether planes 2 x+y+z-1=0,-x+3 y-2 z-3=0 and 3 x-y=-1 intersect. If yes, find the intersection. 0 answers 156 views Determine whether planes 2 x+y+z-1=0,-x+3 y-2 z-3=0 and 3 x-y=-1 intersect. If yes, find the intersection.Determine whether planes 2 x+y+z-1=0,-x+3 y-2 z-3=0 and 3 x-y=-1 intersect. If yes, find the intersection. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do? 0 answers 51 views A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do?A sailboat travels 100 \mathrm{~m} due north while the wind exerts a force of 500 \mathrm{~N} toward the northeast. How much work does the wind do ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars. 0 answers 63 views Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars.Let $U, V, W$ be orthogonal vectors and let $Z=a U+b V+c W$, where $a, b, c$ are scalars. a) (Pythagoras) Show that $\|Z\|^{2}=a^{2}\|U\|^{2}+b ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 In \(\mathbb{R}^{4}$, compute the distance from the point $(1,-2,0,3)$ to the hyperplane $x_{1}+3 x_{2}-$ $x_{3}+x_{4}=3$. 0 answers 82 views In $\mathbb{R}^{4}$, compute the distance from the point $(1,-2,0,3)$ to the hyperplane $x_{1}+3 x_{2}-$ $x_{3}+x_{4}=3$.In $\mathbb{R}^{4}$, compute the distance from the point $(1,-2,0,3)$ to the hyperplane $x_{1}+3 x_{2}-$ $x_{3}+x_{4}=3$. ... close 1 answer 209 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determıne an equation for the plane that passes through the point (1,1,1) and is parallel to the plane$$ x-3 y-2 z-4=0 $$0 answers 322 views Determıne an equation for the plane that passes through the point (1,1,1) and is parallel to the plane$$ x-3 y-2 z-4=0 $$1. Determıne an equation for the plane that passes through the point (1,1,1) and is parallel to the plane$$ x-3 y-2 z-4=0 $$2. Determine the volum ... close 0 answers 297 views Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with $R \vec{v}=\vec{w}$ and $R \vec{w}=\vec{v}$.Let $\vec{v}$ and $\vec{w}$ be vectors in $\mathbb{R}^{n}$. If $\|\vec{v}\|=\|\vec{w}\|$, show there is an orthogonal matrix $R$ with \(R \v ... close 1 answer 176 views The planes$$ x+2 y-2 z=3 \text { and } 2 x+4 y-4 z=7 $$are parallel since their normals, (1,2,-2) and (2,4,-4), are parallel vectors. Find the distance between these planes.The planes$$ x+2 y-2 z=3 \text { and } 2 x+4 y-4 z=7  are parallel since their normals, $(1,2,-2)$ and $(2,4,-4)$, are parallel vectors. Find the d ...
close