Question

find the distance, d, of $overline{ab}$. a = (-5, 1) b = (1, -3) d = ? d = $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ round to the nearest tenth.

Explanation:

Step1: Identify coordinates

Let $(x_1,y_1)=(-5,1)$ and $(x_2,y_2)=(1, - 3)$.

Step2: Substitute into distance formula

$d=\sqrt{(1-(-5))^{2}+((-3 - 1)^{2})}=\sqrt{(1 + 5)^{2}+(-4)^{2}}$.

Step3: Calculate values inside square - root

$(1 + 5)^{2}=6^{2}=36$ and $(-4)^{2}=16$. So $d=\sqrt{36 + 16}=\sqrt{52}$.

Step4: Simplify and round

$\sqrt{52}\approx7.2$.

Answer:

$7.2$