Question

a certain corner of a room is selected as the origin of a rectangular coordinate system. if a fly is crawling on an adjacent wall at a point having coordinates (1.4, 0.8), where the units are meters, what is the distance of the fly from the corner of the room? m

Explanation:

Step1: Identify the distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a two - dimensional rectangular coordinate system is given by the formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). In this case, the origin is \((0,0)\) and the point where the fly is located is \((1.4,0.8)\), so \( x_1 = 0,y_1 = 0,x_2=1.4,y_2 = 0.8 \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 0,y_1 = 0,x_2 = 1.4,y_2=0.8 \) into the distance formula:
\[

$$\begin{align*} d&=\sqrt{(1.4 - 0)^2+(0.8 - 0)^2}\\ &=\sqrt{(1.4)^2+(0.8)^2}\\ &=\sqrt{1.96 + 0.64}\\ &=\sqrt{2.6} \end{align*}$$

\]
Calculate the square root of \( 2.6 \). \( \sqrt{2.6}\approx1.612 \)

Answer:

The distance of the fly from the corner of the room is approximately \( 1.61 \) meters (or more precisely \( \sqrt{2.6}\approx1.612 \) meters). If we need to present it as an exact form, it is \( \sqrt{2.6} \) meters, and if we need a decimal approximation, it is approximately \( 1.61 \) meters.