Question

example 4: find the distance between the following pair of points. round your answer to the nearest tenth. e(-5,6) and f(-8,4) a(-1,8) and b(3,5)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Calculate distance for points $E(-5,6)$ and $F(-8,4)$

Let $(x_1,y_1)=(-5,6)$ and $(x_2,y_2)=(-8,4)$. Then $x_2 - x_1=-8-(-5)=-3$ and $y_2 - y_1=4 - 6=-2$. So $d_{EF}=\sqrt{(-3)^2+(-2)^2}=\sqrt{9 + 4}=\sqrt{13}\approx3.6$.

Step3: Calculate distance for points $A(-1,8)$ and $B(3,5)$

Let $(x_1,y_1)=(-1,8)$ and $(x_2,y_2)=(3,5)$. Then $x_2 - x_1=3-(-1)=4$ and $y_2 - y_1=5 - 8=-3$. So $d_{AB}=\sqrt{4^2+(-3)^2}=\sqrt{16 + 9}=\sqrt{25}=5.0$.

Answer:

The distance between $E$ and $F$ is approximately $3.6$.
The distance between $A$ and $B$ is $5.0$.