Question

what is the distance between the points (4, 5) and (10, 13) on a coordinate plane?
a. 8 units
b. 10 units
c. 14 units
d. 12 units

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: Substitute the values

Here, $x_1 = 4,y_1 = 5,x_2 = 10,y_2 = 13$. So $d=\sqrt{(10 - 4)^2+(13 - 5)^2}=\sqrt{6^2 + 8^2}$.

Step3: Calculate the squares

$6^2=36$ and $8^2 = 64$, so $d=\sqrt{36+64}$.

Step4: Add the values inside square - root

$36 + 64=100$, so $d=\sqrt{100}$.

Step5: Find the square - root

$\sqrt{100}=10$.

Answer:

B. 10 units