Question

find the length of \\(\overline{ad}\\) with \\(a(2, 8)\\) and \\(d(7, -4)\\).

Explanation:

Step1: Recall the 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, \(x_1 = 2,y_1 = 8,x_2=7,y_2=- 4\).

Step2: Substitute the values into the formula

First, calculate the differences in \(x\) and \(y\) coordinates: \(x_2 - x_1=7 - 2 = 5\), \(y_2 - y_1=-4 - 8=-12\).
Then, square these differences: \((x_2 - x_1)^2 = 5^2=25\), \((y_2 - y_1)^2=(-12)^2 = 144\).
Next, sum these squared values: \(25 + 144=169\).
Finally, take the square root: \(\sqrt{169}=13\).

Answer:

13