What is the distance, in units, from the point
to the line ?

Ask by Bowers Nunez. in the United States

Jan 24,2025

Question

What is the distance, in units, from the point $$ (-3,8) $$ to the line $$ -4 y=8-3 x $$ ?

UpStudy AI · Accepted Answer

To find the distance from the point $$(-3, 8)$$ to the line $$ -4y = 8 - 3x $$, follow these steps:

1. **Rewrite the Line in Standard Form:**

Start by rearranging the given equation:
   $$
   -4y = 8 - 3x \implies 3x - 4y - 8 = 0
   $$
   So, the standard form of the line is:
   $$
   3x - 4y - 8 = 0
   $$

2. **Use the Distance Formula:**

The distance $$d$$ from a point $$(x_0, y_0)$$ to the line $$Ax + By + C = 0$$ is given by:
   $$
   d = \frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}
   $$
   
   Here, $$A = 3$$, $$B = -4$$, $$C = -8$$, and the point $$(x_0, y_0) = (-3, 8)$$.

3. **Plug in the Values:**
   
   $$
   d = \frac{|3(-3) + (-4)(8) - 8|}{\sqrt{3^2 + (-4)^2}} = \frac{|-9 - 32 - 8|}{\sqrt{9 + 16}} = \frac{|-49|}{5} = \frac{49}{5}
   $$

So, the distance from the point $$(-3, 8)$$ to the line is $$\frac{49}{5}$$ units.

**Answer:** $$\boxed{\dfrac{49}{5}}$$
The distance from the point $$(-3, 8)$$ to the line $$ -4y = 8 - 3x $$ is $$\frac{49}{5}$$ units.

What is the distance, in units, from the point
to the line ?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Geometry Questions

What is the distance, in units, from the point to the line ?