Question

find the distance between (0, - 7) and (4,6).
the distance is
(round to two decimal places as needed.)

Explanation:

Step1: Identify 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: Assign values

Let $(x_1,y_1)=(0, - 7)$ and $(x_2,y_2)=(4,6)$. Then $x_2 - x_1=4 - 0 = 4$ and $y_2 - y_1=6-( - 7)=6 + 7 = 13$.

Step3: Calculate squares

$(x_2 - x_1)^2=4^2 = 16$ and $(y_2 - y_1)^2=13^2 = 169$.

Step4: Sum of squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 169=185$.

Step5: Find distance

$d=\sqrt{185}\approx13.60$

Answer:

$13.60$