Question

calculate the distance between the two points shown on the graph below. give your answer correct to 2 decimal places if necessary.
y
12
10
8
b(4,8)
6
4
2
a(5,2)
2 4 6 8 10 12
x

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, let $(x_1,y_1)=(4,8)$ and $(x_2,y_2)=(5,2)$.

Step2: Calculate differences

$x_2 - x_1=5 - 4 = 1$ and $y_2 - y_1=2 - 8=-6$.

Step3: Square the differences

$(x_2 - x_1)^2=1^2 = 1$ and $(y_2 - y_1)^2=(-6)^2 = 36$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=1 + 36=37$.

Step5: Calculate the distance

$d=\sqrt{37}\approx6.08$.

Answer:

$6.08$