Question

find the distance, d, of $overline{ab}$. a = (-3, 4) b = (5, 8) d = ? d = $sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ round to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(-3,4)$ and $(x_2,y_2)=(5,8)$.

Step2: Substitute into distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{(5-(-3))^2+(8 - 4)^2}$.

Step3: Simplify the expressions inside the square - root

First, $5-(-3)=5 + 3=8$ and $8 - 4 = 4$. Then $d=\sqrt{8^2+4^2}=\sqrt{64 + 16}$.

Step4: Calculate the sum inside the square - root

$64+16 = 80$, so $d=\sqrt{80}$.

Step5: Simplify the square - root and round

$\sqrt{80}\approx8.944\approx8.9$.

Answer:

$8.9$