Question

find the distance from point w to (overleftrightarrow{yz}). if necessary, round your answer to the nearest tenth place. y(-4, 3) x(-2, 1) w(4, 1) z(1, -2)

Explanation:

Step1: Find the equation of line YZ

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $Y(-4,3)$ and $Z(1,-2)$, $m=\frac{-2 - 3}{1-(-4)}=\frac{-5}{5}=-1$.
Using the point - slope form $y - y_1=m(x - x_1)$ with point $Z(1,-2)$, we have $y+2=-1(x - 1)$, which simplifies to $x + y+1 = 0$.

Step2: Use the distance formula from a point to a line

The distance $d$ from a point $(x_0,y_0)$ to a line $Ax+By + C = 0$ is given by $d=\frac{\vert Ax_0+By_0 + C\vert}{\sqrt{A^2 + B^2}}$.
For point $W(4,-1)$ and line $x + y+1 = 0$ (where $A = 1$, $B = 1$, $C = 1$, $x_0=4$, $y_0=-1$), we have $d=\frac{\vert1\times4+1\times(-1)+1\vert}{\sqrt{1^2+1^2}}=\frac{\vert4 - 1+1\vert}{\sqrt{2}}=\frac{4}{\sqrt{2}}=2\sqrt{2}\approx2.8$.

Answer:

$2.8$ units